Nagoya Mathematical Journal最新文献

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ON A COMPARISON BETWEEN DWORK AND RIGID COHOMOLOGIES OF PROJECTIVE COMPLEMENTS 射影补的网络与刚性上同的比较

IF 0.8 2区数学 Q3 Mathematics

Nagoya Mathematical Journal

Pub Date : 2023-12-01 DOI: 10.1017/nmj.2023.32

JUNYEONG PARK

For homogeneous polynomials

$G_1,ldots ,G_k$

over a finite field, their Dwork complex is defined by Adolphson and Sperber, based on Dwork’s theory. In this article, we will construct an explicit cochain map from the Dwork complex of

$G_1,ldots ,G_k$

to the Monsky–Washnitzer complex associated with some affine bundle over the complement

$mathbb {P}^nsetminus X_G$

of the common zero

$X_G$

$G_1,ldots ,G_k$

, which computes the rigid cohomology of

$mathbb {P}^nsetminus X_G$

. We verify that this cochain map realizes the rigid cohomology of

$mathbb {P}^nsetminus X_G$

as a direct summand of the Dwork cohomology of

$G_1,ldots ,G_k$

. We also verify that the comparison map is compatible with the Frobenius and the Dwork operator defined on both complexes, respectively. Consequently, we extend Katz’s comparison results in [19] for projective hypersurface complements to arbitrary projective complements.

对于有限域上的齐次多项式$G_1，ldots,G_k$，它们的Dwork复形由Adolphson和Sperber根据Dwork理论定义。在本文中，我们将构造一个显式的协链映射，从$G_1，ldots,G_k$的Dwork复形到$G_1，ldots,G_k$的公零$X_G$的补$mathbb {P} n set- X_G$上与某个仿射束相关联的Monsky-Washnitzer复形，计算$mathbb {P} n set- X_G$的刚性上同调。我们证明了这个协链映射实现了$mathbb {P}^n set- X_G$的刚性上同调作为$G_1，ldots,G_k$的Dwork上同调的直接和。我们还验证了比较映射分别与两个复合体上定义的Frobenius算子和Dwork算子兼容。因此，我们将Katz在[19]中关于射影超曲面补的比较结果推广到任意射影补。

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引用次数: 0

HOW TO EXTEND CLOSURE AND INTERIOR OPERATIONS TO MORE MODULES 如何将闭包和内部操作扩展到更多模块

IF 0.8 2区数学 Q3 Mathematics

Nagoya Mathematical Journal

Pub Date : 2023-12-01 DOI: 10.1017/nmj.2023.36

NEIL EPSTEIN, REBECCA R. G., JANET VASSILEV

There are several ways to convert a closure or interior operation to a different operation that has particular desirable properties. In this paper, we axiomatize three ways to do so, drawing on disparate examples from the literature, including tight closure, basically full closure, and various versions of integral closure. In doing so, we explore several such desirable properties, including hereditary, residual, and cofunctorial, and see how they interact with other properties such as the finitistic property.

有几种方法可以将闭包或内部操作转换为具有特定期望属性的不同操作。在本文中，我们公化了三种方法来做到这一点，从文献中吸取不同的例子，包括紧闭包，基本完全闭包和各种版本的积分闭包。在这样做的过程中，我们探索了几个这样的理想性质，包括遗传、剩余和共同的，并看到它们如何与其他性质(如有限性质)相互作用。

引用次数: 1

GENUS CURVES WITH BAD REDUCTION AT ONE ODD PRIME 在一个奇素数处约化不良的属曲线

IF 0.8 2区数学 Q3 Mathematics

Nagoya Mathematical Journal

Pub Date : 2023-11-29 DOI: 10.1017/nmj.2023.35

ANDRZEJ DĄBROWSKI, MOHAMMAD SADEK

The problem of classifying elliptic curves over

$mathbb Q$

with a given discriminant has received much attention. The analogous problem for genus

$2$

curves has only been tackled when the absolute discriminant is a power of

$2$

. In this article, we classify genus

$2$

curves C defined over

${mathbb Q}$

with at least two rational Weierstrass points and whose absolute discriminant is an odd prime. In fact, we show that such a curve C must be isomorphic to a specialization of one of finitely many

$1$

-parameter families of genus

$2$

curves. In particular, we provide genus

$2$

analogues to Neumann–Setzer families of elliptic curves over the rationals.

用给定的判别式对$mathbb Q$上的椭圆曲线进行分类的问题受到了广泛的关注。对于$2$曲线的类似问题，只有在绝对判别式是$2$的幂次时才得到解决。在这篇文章中，我们对定义在${mathbb Q}$上的$2$曲线C进行了分类，这些曲线C至少有两个有理Weierstrass点，其绝对判别式是奇素数。事实上，我们证明了这样的曲线C必须同构于有限多个$1$参数族的$2$曲线中的一个的专门化。特别地，我们提供了在有理数上的椭圆曲线的Neumann-Setzer族的属$2类似物。

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引用次数: 0

NMJ volume 252 Cover and Back matter NMJ卷252封面和封底

2区数学 Q3 Mathematics

Nagoya Mathematical Journal

Pub Date : 2023-10-31 DOI: 10.1017/nmj.2023.31

An abstract is not available for this content so a preview has been provided. As you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

此内容的摘要不可用，因此提供了预览。当您可以访问此内容时，可以通过“保存PDF”操作按钮获得完整的PDF。

引用次数: 0

NMJ volume 252 Cover and Front matter NMJ卷252封面和正面问题

2区数学 Q3 Mathematics

Nagoya Mathematical Journal

Pub Date : 2023-10-31 DOI: 10.1017/nmj.2023.30

引用次数: 0

NON-ISOMORPHIC SMOOTH COMPACTIFICATIONS OF THE MODULI SPACE OF CUBIC SURFACES 三次曲面模空间的非同构光滑紧化

2区数学 Q3 Mathematics

Nagoya Mathematical Journal

Pub Date : 2023-10-03 DOI: 10.1017/nmj.2023.27

SEBASTIAN CASALAINA-MARTIN, SAMUEL GRUSHEVSKY, KLAUS HULEK, RADU LAZA

Abstract The well-studied moduli space of complex cubic surfaces has three different, but isomorphic, compact realizations: as a GIT quotient ${mathcal {M}}^{operatorname {GIT}}$ , as a Baily–Borel compactification of a ball quotient ${(mathcal {B}_4/Gamma )^*}$ , and as a compactified K -moduli space. From all three perspectives, there is a unique boundary point corresponding to non-stable surfaces. From the GIT point of view, to deal with this point, it is natural to consider the Kirwan blowup ${mathcal {M}}^{operatorname {K}}rightarrow {mathcal {M}}^{operatorname {GIT}}$ , whereas from the ball quotient point of view, it is natural to consider the toroidal compactification ${overline {mathcal {B}_4/Gamma }}rightarrow {(mathcal {B}_4/Gamma )^*}$ . The spaces ${mathcal {M}}^{operatorname {K}}$ and ${overline {mathcal {B}_4/Gamma }}$ have the same cohomology, and it is therefore natural to ask whether they are isomorphic. Here, we show that this is in fact not the case. Indeed, we show the more refined statement that ${mathcal {M}}^{operatorname {K}}$ and ${overline {mathcal {B}_4/Gamma }}$ are equivalent in the Grothendieck ring, but not K -equivalent. Along the way, we establish a number of results and techniques for dealing with singularities and canonical classes of Kirwan blowups and toroidal compactifications of ball quotients.

复杂三次曲面的模空间有三种不同但同构的紧化实现:作为GIT商${mathcal {M}}^{operatorname {GIT}}$，作为球商的Baily-Borel紧化${(mathcal {B}_4/Gamma )^*}$，以及作为紧化K模空间。从这三个角度来看，存在一个与非稳定曲面相对应的唯一边界点。从GIT的角度来看，要处理这一点，很自然地考虑Kirwan爆破${mathcal {M}}^{operatorname {K}}rightarrow {mathcal {M}}^{operatorname {GIT}}$，而从球商的角度来看，很自然地考虑环面紧化${overline {mathcal {B}_4/Gamma }}rightarrow {(mathcal {B}_4/Gamma )^*}$。空间${mathcal {M}}^{operatorname {K}}$和${overline {mathcal {B}_4/Gamma }}$具有相同的上同调，因此很自然地要问它们是否同构。在这里，我们证明事实并非如此。事实上，我们给出了一个更精确的表述，即${mathcal {M}}^{operatorname {K}}$和${overline {mathcal {B}_4/Gamma }}$在格罗滕迪克环中是等价的，但不是K等价的。在此过程中，我们建立了一些处理奇异性和正则类的结果和技术，以及球商的环面紧化。

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引用次数: 1

EXACT SUBCATEGORIES, SUBFUNCTORS OF , AND SOME APPLICATIONS 精确的子类别、子函子和一些应用程序

2区数学 Q3 Mathematics

Nagoya Mathematical Journal

Pub Date : 2023-09-27 DOI: 10.1017/nmj.2023.29

HAILONG DAO, SOUVIK DEY, MONALISA DUTTA

Abstract Let $({cal{A}},{cal{E}})$ be an exact category. We establish basic results that allow one to identify sub(bi)functors of ${operatorname{Ext}}_{cal{E}}(-,-)$ using additivity of numerical functions and restriction to subcategories. We also study a small number of these new functors over commutative local rings in detail and find a range of applications from detecting regularity to understanding Ulrich modules.

摘要设$({cal{A}}，{cal{E}})$是一个精确范畴。利用数值函数的可加性和对子范畴的限制，建立了可以识别${operatorname{Ext}}_{cal{E}}(-，-)$的子(bi)函子的基本结果。我们还详细研究了交换局部环上的少量这些新函子，并发现了从检测正则性到理解Ulrich模的一系列应用。

引用次数: 2

A BALL QUOTIENT PARAMETRIZING TRIGONAL GENUS 4 CURVES 一个球商参数化的三角形格4曲线

2区数学 Q3 Mathematics

Nagoya Mathematical Journal

Pub Date : 2023-09-21 DOI: 10.1017/nmj.2023.28

EDUARD LOOIJENGA

Abstract We consider the moduli space of genus 4 curves endowed with a $g^1_3$ (which maps with degree 2 onto the moduli space of genus 4 curves). We prove that it defines a degree $frac {1}{2}(3^{10}-1)$ cover of the nine-dimensional Deligne–Mostow ball quotient such that the natural divisors that live on that moduli space become totally geodesic (their normalizations are eight-dimensional ball quotients). This isomorphism differs from the one considered by S. Kondō, and its construction is perhaps more elementary, as it does not involve K3 surfaces and their Torelli theorem: the Deligne–Mostow ball quotient parametrizes certain cyclic covers of degree 6 of a projective line and we show how a level structure on such a cover produces a degree 3 cover of that line with the same discriminant, yielding a genus 4 curve endowed with a $g^1_3$ .

摘要考虑了赋$g^1_3$的4格曲线的模空间(它以2次映射到4格曲线的模空间上)。我们证明了它定义了一个度$frac{1}{2}(3^{10}-1)$覆盖的九维delignee - mostow球商，使得在该模空间上的自然因子成为完全测地的(它们的归一化是八维球商)。这种同构不同于S. kondji所考虑的同构，它的构造可能更基本，因为它不涉及K3曲面和它们的Torelli定理:delignee - mostow球商参数化了投影线的某些6次循环覆盖，我们展示了这样一个覆盖上的水平结构如何产生该线的3次覆盖，具有相同的判别，产生具有$g^1_3$的4属曲线。

引用次数: 0

NEW MODULI SPACES OF ONE-DIMENSIONAL SHEAVES ON 上一维轮轴的新模空间

2区数学 Q3 Mathematics

Nagoya Mathematical Journal

Pub Date : 2023-09-18 DOI: 10.1017/nmj.2023.26

DAPENG MU

Abstract We define a one-dimensional family of Bridgeland stability conditions on $mathbb {P}^n$ , named “Euler” stability condition. We conjecture that the “Euler” stability condition converges to Gieseker stability for coherent sheaves. Here, we focus on ${mathbb P}^3$ , first identifying Euler stability conditions with double-tilt stability conditions, and then we consider moduli of one-dimensional sheaves, proving some asymptotic results, boundedness for walls, and then explicitly computing walls and wall-crossings for sheaves supported on rational curves of degrees $3$ and $4$ .

摘要在$mathbb {P}^n$上定义了一类一维桥地稳定性条件，称为“欧拉”稳定性条件。我们推测相干轴的“欧拉”稳定性条件收敛于Gieseker稳定性。本文以${mathbb P}^3$为中心，首先确定了具有双倾斜稳定性条件的欧拉稳定条件，然后考虑了一维滑轮的模，证明了一些渐近结果，证明了墙体的有界性，然后显式地计算了在$3$和$4$有理曲线上支撑的滑轮的墙体和过墙。

引用次数: 0

MULTIPLIERS AND CHARACTERIZATION OF THE DUAL OF NEVANLINNA-TYPE SPACES nevanlinna型空间的乘数和对偶的表征

IF 0.8 2区数学 Q3 Mathematics

Nagoya Mathematical Journal

Pub Date : 2023-09-07 DOI: 10.1017/nmj.2023.24

Mieczysław Mastyło, Bartosz Staniów

The Nevanlinna-type spaces

$N_varphi $

of analytic functions on the disk in the complex plane generated by strongly convex functions

$varphi $

in the sense of Rudin are studied. We show for some special class of strongly convex functions asymptotic bounds on the growth of the Taylor coefficients of a function in

$N_varphi $

and use these to characterize the coefficient multipliers from

$N_varphi $

into the Hardy spaces

$H^p$

with

. As a by-product, we prove a representation of continuous linear functionals on

$N_varphi $

研究了由Rudin意义上的强凸函数$varphi $生成的复平面圆盘上解析函数的nevanlinna型空间$N_varphi $。对于一类特殊的强凸函数，我们给出了函数在$N_varphi $中泰勒系数增长的渐近界，并利用这些渐近界刻画了从$N_varphi $到$H^p$的Hardy空间的系数乘子。作为副产品，我们证明了连续线性泛函在$N_varphi $上的表示。

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引用次数: 0

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