Journal of Algebraic Geometry最新文献

英文中文

The class of the affine line is a zero divisor in the Grothendieck ring 仿射线的类是格罗滕迪克环上的一个零因子

IF 1.8 1区数学 Q2 MATHEMATICS

Journal of Algebraic Geometry

Pub Date : 2017-01-01 DOI: 10.7282/T33B62H9

L. Borisov

引用次数: 100

Algebraic approximations of fibrations in abelian varieties over a curve 曲线上阿贝尔变异中纤颤的代数近似

IF 1.8 1区数学 Q2 MATHEMATICS

Journal of Algebraic Geometry

Pub Date : 2016-12-29 DOI: 10.1090/jag/791

Hsueh-Yung Lin

For every fibration f : X → B f : X to B with X X a compact Kähler manifold, B B a smooth projective curve, and a general fiber of f f an abelian variety, we prove that f f has an algebraic approximation.

对于每一个纤维f: X→B f: X 到B，其中X X是紧的Kähler流形，B B是光滑的投影曲线，f f是一个一般的纤维和阿贝尔变，我们证明了f f有一个代数逼近。

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引用次数: 7

Diagonalisable $p$-groups cannot fix exactly one point on projective varieties 可对角化的p群不能在射影变体上精确地固定一个点

IF 1.8 1区数学 Q2 MATHEMATICS

Journal of Algebraic Geometry

Pub Date : 2016-12-22 DOI: 10.1090/jag/749

Olivier Haution

We prove an algebraic version of classical theorem in topology, asserting that an abelian p-group action on a smooth projective variety of positive dimension cannot fix exactly one point. When the group has only two elements, we prove that the number of fixed points cannot be odd. The main tool is a construction originally used by Rost in the context of the degree formula. The framework of diagonalisable groups allows us to include the case of base fields of characteristic p.

我们证明了经典拓扑学定理的一个代数版本，证明了正维光滑射影变化上的阿贝尔p群作用不能精确地固定一个点。当群只有两个元素时，我们证明了不动点的个数不能是奇数。主要工具是Rost最初在度公式中使用的结构。可对角群的框架允许我们考虑特征p的基域的情况。

引用次数: 2

Images of manifolds with semi-ample anti-canonical divisor 具有半样本反正则因子的流形的象

IF 1.8 1区数学 Q2 MATHEMATICS

Journal of Algebraic Geometry

Pub Date : 2016-11-18 DOI: 10.1090/JAG/662

C. Birkar, Yifei Chen

We prove that if f : X → Z is a smooth surjective morphism between projective manifolds and if −KX is semi-ample, then −KZ is also semi-ample. This was conjectured by Fujino and Gongyo. We list several counter-examples to show that this fails without the smoothness assumption on f . We prove the above result by proving some results concerning the moduli divisor of the canonical bundle formula associated to a klt-trivial fibration (X,B)→ Z.

证明了如果f: X→Z是射影流形间的光滑满射态射，如果- KX是半样本，则- KZ也是半样本。这是Fujino和Gongyo推测的。我们列出了几个反例来证明，如果没有f的平滑假设，这种方法就失败了。我们通过证明与klt-平凡纤维(X,B)→Z相关的正则束公式的模因子的一些结果来证明上述结果。

引用次数: 10

Gorenstein modifications and mathds{𝑄}-Gorenstein rings Gorenstein修正和数学{𝑄}-Gorenstein环

IF 1.8 1区数学 Q2 MATHEMATICS

Journal of Algebraic Geometry

Pub Date : 2016-11-13 DOI: 10.1090/JAG/760

Hailong Dao, O. Iyama, Ryo Takahashi, M. Wemyss

Let <inline-formula content-type="math/mathml"><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper R"> <mml:semantics> <mml:mi>R</mml:mi> <mml:annotation encoding="application/x-tex">R</mml:annotation> </mml:semantics></mml:math></inline-formula> be a Cohen–Macaulay normal domain with a canonical module <inline-formula content-type="math/mathml"><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="omega Subscript upper R"> <mml:semantics> <mml:msub> <mml:mi>ω</mml:mi> <mml:mi>R</mml:mi> </mml:msub> <mml:annotation encoding="application/x-tex">omega _R</mml:annotation> </mml:semantics></mml:math></inline-formula>. It is proved that if <inline-formula content-type="math/mathml"><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper R"> <mml:semantics> <mml:mi>R</mml:mi> <mml:annotation encoding="application/x-tex">R</mml:annotation> </mml:semantics></mml:math></inline-formula> admits a noncommutative crepant resolution (NCCR), then necessarily it is <inline-formula content-type="math/mathml"><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="double-struck upper Q"> <mml:semantics> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="double-struck">Q</mml:mi> </mml:mrow> <mml:annotation encoding="application/x-tex">mathds {Q}</mml:annotation> </mml:semantics></mml:math></inline-formula>-Gorenstein. Writing <inline-formula content-type="math/mathml"><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper S"> <mml:semantics> <mml:mi>S</mml:mi> <mml:annotation encoding="application/x-tex">S</mml:annotation> </mml:semantics></mml:math></inline-formula> for a Zariski local canonical cover of <inline-formula content-type="math/mathml"><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper R"> <mml:semantics> <mml:mi>R</mml:mi> <mml:annotation encoding="application/x-tex">R</mml:annotation> </mml:semantics></mml:math></inline-formula>, a tight relationship between the existence of noncommutative (crepant) resolutions on <inline-formula content-type="math/mathml"><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper R"> <mml:semantics> <mml:mi>R</mml:mi> <mml:annotation encoding="application/x-tex">R</mml:annotation> </mml:semantics></mml:math></inline-formula> and <inline-formula content-type="math/mathml"><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper S"> <mml:semantics> <mml:mi>S</mml:mi> <mml:annotation encoding="application/x-tex">S</mml:annotation> </mml:semantics></mml:math></inline-formula> is given. A weaker notion of Gorenstein modification is developed, and a similar tight relationship is given. There are three applications: non-Gorenstein quotient singularities by connected reductive groups cannot admit an NCCR, the centre of any NCCR is log-termin

设R R是一个柯恩-麦考利正规定义域，其正则模为R。证明了如果R R允许非交换蠕变分解(NCCR)，则它必然是Q mathds {Q} -Gorenstein。对R R的Zariski局部正则盖写S S，给出了R R上非交换(渐变)分辨的存在性与S S之间的紧密关系。提出了一个较弱的Gorenstein修正概念，并给出了一个类似的紧密关系。有三种应用:连通约化群的非gorenstein商奇点不允许存在NCCR，任何NCCR的中心都是log-terminal，二维cm有限代数的Auslander-Esnault分类可以由Buchweitz-Greuel-Schreyer导出。

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引用次数: 5

Spaces with 𝔾_{𝕞}-action, hyperbolic localization and nearby cycles 具有几何作用、双曲定位和邻近环的空间

IF 1.8 1区数学 Q2 MATHEMATICS

Journal of Algebraic Geometry

Pub Date : 2016-11-05 DOI: 10.1090/jag/710

Timo Richarz

We study families of algebraic spaces with G m {mathbb G}_m -action and prove Braden’s theorem on hyperbolic localization for arbitrary base schemes. As an application, we obtain that hyperbolic localization commutes with nearby cycles.

研究了具有G m {mathbb G}_m -作用的代数空间族，并证明了任意基格式双曲局部化的Braden定理。作为一个应用，我们得到了双曲局部化与附近环的交换。

引用次数: 21

Algebraic stratified general position and transversality 代数分层一般位置与横向

IF 1.8 1区数学 Q2 MATHEMATICS

Journal of Algebraic Geometry

Pub Date : 2016-10-05 DOI: 10.1090/JAG/713

C. McCrory, A. Parusiński, L. Paunescu

The method of Whitney interpolation is used to construct, for any real or complex projective algebraic variety, a stratified submersive family of self-maps that yields stratified general position and transversality theorems for semialgebraic subsets.

惠特尼插值的方法被用来构造，对于任何实数或复数射影代数变量，自映射的分层淹没族，产生半代数子集的分层一般位置定理和横贯定理。

引用次数: 3

Minimal plane valuations 最小平面估值

IF 1.8 1区数学 Q2 MATHEMATICS

Journal of Algebraic Geometry

Pub Date : 2016-09-16 DOI: 10.1090/JAG/722

C. Galindo, F. Monserrat, Julio Jos'e Moyano-Fern'andez

We consider the value <inline-formula content-type="math/mathml"><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="ModifyingAbove mu With caret left-parenthesis nu right-parenthesis equals limit Underscript m right-arrow normal infinity Endscripts m Superscript negative 1 Baseline a left-parenthesis m upper L right-parenthesis"> <mml:semantics> <mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mover> <mml:mi>μ</mml:mi> <mml:mo stretchy="false">^</mml:mo> </mml:mover> </mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mi>ν</mml:mi> <mml:mo stretchy="false">)</mml:mo> <mml:mo>=</mml:mo> <mml:munder> <mml:mo movablelimits="true" form="prefix">lim</mml:mo> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi>m</mml:mi> <mml:mo stretchy="false">→</mml:mo> <mml:mi mathvariant="normal">∞</mml:mi> </mml:mrow> </mml:munder> <mml:msup> <mml:mi>m</mml:mi> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> <mml:mi>a</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>m</mml:mi> <mml:mi>L</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">hat {mu } (nu ) = lim _{m rightarrow infty } m^{-1} a(mL)</mml:annotation> </mml:semantics></mml:math></inline-formula>, where <inline-formula content-type="math/mathml"><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="a left-parenthesis m upper L right-parenthesis"> <mml:semantics> <mml:mrow> <mml:mi>a</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>m</mml:mi> <mml:mi>L</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">a(mL)</mml:annotation> </mml:semantics></mml:math></inline-formula> is the last value of the vanishing sequence of <inline-formula content-type="math/mathml"><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper H Superscript 0 Baseline left-parenthesis m upper L right-parenthesis"> <mml:semantics> <mml:mrow> <mml:msup> <mml:mi>H</mml:mi> <mml:mn>0</mml:mn> </mml:msup> <mml:mo stretchy="false">(</mml:mo> <mml:mi>m</mml:mi> <mml:mi>L</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">H^0(mL)</mml:annotation> </mml:semantics></mml:math></inline-formula> along a divisorial or irrational valuation <inline-formula content-type="math/mathml"><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="nu"> <mml:semantics> <mml:mi>ν</mml:mi> <mml:annotation encoding="application/x-tex">nu</mml:annotation> </mml:semantics></m

我们考虑μ ^ (ν) = lim m→∞m−1 a (m L) hat {mu } （nu ) = lim ＿{m rightarrow infty } m^{－１} a(mL)，其中a(mL) a(mL)是h0 (mL) H^0(mL)沿一个除数或无理数值ν的消失序列的最后值 nu 以O p2, P为中心 mathcal {o}＿{mathbb {p}^2,p} ， L L(分别为p p)为射影平面p2的直线(分别为点) mathbb {p}^2在代数闭域上。对于赋值，该值包含与由点的Seshadri常数给出的信息相似的信息。μ ^ (ν)≥1 / v o l (ν) hat {mu } （nu ） geq sqrt {1 / mathrm {vol}（nu ）} 最小值是那些满足等式的值。在本文中，我们证明了Greuel-Lossen-Shustin猜想隐含了涉及最小值的Nagata猜想的一个变体，它扩展了[Comm. Anal]中所述的一个变体。(Geom. 25 (2017)， pp. 125-161)，这也暗示了原始的长田猜想。我们还提供了具有任意数目的普塞指数的无限多极小极一般值族，并给出了一个渐近结果，可作为上述猜想方向的证据。

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引用次数: 9

Uniqueness of embeddings of the affine line into algebraic groups 仿射线嵌入代数群的唯一性

IF 1.8 1区数学 Q2 MATHEMATICS

Journal of Algebraic Geometry

Pub Date : 2016-09-07 DOI: 10.1090/JAG/725

P. Feller, Immanuel Stampfli

Let <inline-formula content-type="math/mathml"><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper Y"> <mml:semantics> <mml:mi>Y</mml:mi> <mml:annotation encoding="application/x-tex">Y</mml:annotation> </mml:semantics></mml:math></inline-formula> be the underlying variety of a complex connected affine algebraic group. We prove that two embeddings of the affine line <inline-formula content-type="math/mathml"><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="double-struck upper C"> <mml:semantics> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="double-struck">C</mml:mi> </mml:mrow> <mml:annotation encoding="application/x-tex">mathbb {C}</mml:annotation> </mml:semantics></mml:math></inline-formula> into <inline-formula content-type="math/mathml"><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper Y"> <mml:semantics> <mml:mi>Y</mml:mi> <mml:annotation encoding="application/x-tex">Y</mml:annotation> </mml:semantics></mml:math></inline-formula> are the same up to an automorphism of <inline-formula content-type="math/mathml"><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper Y"> <mml:semantics> <mml:mi>Y</mml:mi> <mml:annotation encoding="application/x-tex">Y</mml:annotation> </mml:semantics></mml:math></inline-formula> provided that <inline-formula content-type="math/mathml"><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper Y"> <mml:semantics> <mml:mi>Y</mml:mi> <mml:annotation encoding="application/x-tex">Y</mml:annotation> </mml:semantics></mml:math></inline-formula> is not isomorphic to a product of a torus <inline-formula content-type="math/mathml"><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="left-parenthesis double-struck upper C Superscript asterisk Baseline right-parenthesis Superscript k"> <mml:semantics> <mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:msup> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="double-struck">C</mml:mi> </mml:mrow> <mml:mo>∗</mml:mo> </mml:msup> <mml:msup> <mml:mo stretchy="false">)</mml:mo> <mml:mi>k</mml:mi> </mml:msup> </mml:mrow> <mml:annotation encoding="application/x-tex">(mathbb {C}^ast )^k</mml:annotation> </mml:semantics></mml:math></inline-formula> and one of the three varieties <inline-formula content-type="math/mathml"><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="double-struck upper C cubed"> <mml:semantics> <mml:msup> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="double-struck">C</mml:mi> </mml:mrow> <mml:mn>3</mml:mn> </mml:msup> <mml:annotation encoding="application/x-tex">mathbb {C}^3</mml:annotation> </mml:semantics></mml:math></inline-formula>, <inline-formula content-type="math/mathml"><mml:m

设Y Y为复连通仿射代数群的基变。我们证明了仿射线C mathbb {C}在Y Y中的两个嵌入是相同的，直到Y Y的自同构，条件是Y Y不同构于环面(C∗)k (mathbb {C}^ast)^k与三个变体c3 mathbb {C}^3, SL 2 operatorname {SL}_2，和PSL 2 operatorname {PSL}_2。

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引用次数: 8

Stable rationality of orbifold Fano 3-fold hypersurfaces 轨道Fano三重超曲面的稳定合理性

IF 1.8 1区数学 Q2 MATHEMATICS

Journal of Algebraic Geometry

Pub Date : 2016-08-03 DOI: 10.1090/JAG/712

Takuzo Okada

We determine the rationality of very general quasi-smooth Fano 3 3 -fold weighted hypersurfaces completely and determine the stable rationality of them except for cubic 3 3 -folds. More precisely we prove that (i) very general Fano 3 3 -fold weighted hypersurfaces of index 1 1 or 2 2 are not stably rational except possibly for the cubic 3-folds, (ii) among the 27 27 families of Fano 3-fold weighted hypersurfaces of index greater than 2 2 , very general members of 7 7 specific families are not stably rational, and the remaining 20 20 families consist of rational varieties.

完整地确定了非常一般的拟光滑Fano 3 - 3折加权超曲面的合理性，并确定了除三次3 - 3折外的其他超曲面的稳定合理性。更确切地说，我们证明了(i)指数11或22的非常一般的Fano 3-fold加权超曲面除了可能的三次3-fold外，是不稳定有理的;(ii)指数大于22的Fano 3-fold加权超曲面的2727个族中，有77个特定族的非常一般的成员是不稳定有理的，其余2020个族由有理变种组成。

{"title":"Stable rationality of orbifold Fano 3-fold hypersurfaces","authors":"Takuzo Okada","doi":"10.1090/JAG/712","DOIUrl":"https://doi.org/10.1090/JAG/712","url":null,"abstract":"We determine the rationality of very general quasi-smooth Fano <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"3\">\u0000 <mml:semantics>\u0000 <mml:mn>3</mml:mn>\u0000 <mml:annotation encoding=\"application/x-tex\">3</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>-fold weighted hypersurfaces completely and determine the stable rationality of them except for cubic <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"3\">\u0000 <mml:semantics>\u0000 <mml:mn>3</mml:mn>\u0000 <mml:annotation encoding=\"application/x-tex\">3</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>-folds. More precisely we prove that (i) very general Fano <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"3\">\u0000 <mml:semantics>\u0000 <mml:mn>3</mml:mn>\u0000 <mml:annotation encoding=\"application/x-tex\">3</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>-fold weighted hypersurfaces of index <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"1\">\u0000 <mml:semantics>\u0000 <mml:mn>1</mml:mn>\u0000 <mml:annotation encoding=\"application/x-tex\">1</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> or <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"2\">\u0000 <mml:semantics>\u0000 <mml:mn>2</mml:mn>\u0000 <mml:annotation encoding=\"application/x-tex\">2</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> are not stably rational except possibly for the cubic 3-folds, (ii) among the <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"27\">\u0000 <mml:semantics>\u0000 <mml:mn>27</mml:mn>\u0000 <mml:annotation encoding=\"application/x-tex\">27</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> families of Fano 3-fold weighted hypersurfaces of index greater than <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"2\">\u0000 <mml:semantics>\u0000 <mml:mn>2</mml:mn>\u0000 <mml:annotation encoding=\"application/x-tex\">2</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>, very general members of <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"7\">\u0000 <mml:semantics>\u0000 <mml:mn>7</mml:mn>\u0000 <mml:annotation encoding=\"application/x-tex\">7</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> specific families are not stably rational, and the remaining <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"20\">\u0000 <mml:semantics>\u0000 <mml:mn>20</mml:mn>\u0000 <mml:annotation encoding=\"application/x-tex\">20</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> families consist of rational varieties.","PeriodicalId":54887,"journal":{"name":"Journal of Algebraic Geometry","volume":"1 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2016-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1090/JAG/712","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"60550485","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 13

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Journal of Algebraic Geometry

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