Transactions of the American Mathematical Society, Series B最新文献_第9页

The Torelli map restricted to the hyperelliptic locus 托雷利图局限于超椭圆轨迹

Transactions of the American Mathematical Society, Series B

Pub Date : 2019-11-05 DOI: 10.1090/BTRAN/64

Aaron Landesman

Let g ≥ 2 g geq 2 and let the Torelli map denote the map sending a genus g g curve to its principally polarized Jacobian. We show that the restriction of the Torelli map to the hyperelliptic locus is an immersion in characteristic not 2 2 . In characteristic 2 2 , we show the Torelli map restricted to the hyperelliptic locus fails to be an immersion because it is generically inseparable; moreover, the induced map on tangent spaces has kernel of dimension g − 2 g-2 at every point.

设g≥2g geq 2，并设Torelli映射表示将g属曲线发送到其主极化雅可比矩阵的映射。我们证明了Torelli映射对超椭圆轨迹的限制是对特征非22的浸没。在特征22中，我们证明了局限于超椭圆轨迹的Torelli映射不能成为浸没，因为它是一般不可分的;此外，切空间上的诱导映射在每一点上都具有g−2 g-2维核。

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引用次数: 7

Homomorphism obstructions for satellite maps 卫星地图的同态障碍

Transactions of the American Mathematical Society, Series B

Pub Date : 2019-10-08 DOI: 10.1090/btran/123

Allison N. Miller

A knot in a solid torus defines a map on the set of (smooth or topological) concordance classes of knots in S 3 S^3 . This set admits a group structure, but a conjecture of Hedden suggests that satellite maps never induce interesting homomorphisms: we give new evidence for this conjecture in both categories. First, we use Casson-Gordon signatures to give the first obstruction to a slice pattern inducing a homomorphism on the topological concordance group, constructing examples with every winding number besides ± 1 pm 1 . We then provide subtle examples of satellite maps which map arbitrarily deep into the n n -solvable filtration of Cochran, Orr, and Teichner [Ann. of Math. (2) 157 (2003), pp. 433–519], act like homomorphisms on arbitrary finite sets of knots, and yet which still do not induce homomorphisms. Finally, we verify Hedden’s conjecture in the smooth category for all small crossing number satellite operators but one.

一个实心环面的结定义了S^3中结的(光滑的或拓扑的)一致性类集合上的映射。这个集合承认一个群结构，但是heden的一个猜想表明卫星图从来不会产生有趣的同态:我们在两个范畴中为这个猜想提供了新的证据。首先，我们使用Casson-Gordon签名给出了在拓扑和谐群上诱导同态的片模式的第一个障碍，构造了除±1 pm 1以外的所有圈数的例子。然后，我们提供了卫星地图的微妙例子，这些卫星地图可以任意深入到Cochran, Orr和Teichner [Ann]的n可解过滤中。的数学。(2) 157 (2003)， pp. 433-519]，在任意有限节集合上表现得像同态，但仍然不诱导同态。最后，我们对除一个卫星运营商外的所有小交叉数卫星运营商在光滑范畴内验证了Hedden猜想。

引用次数: 8

Entropy and dimension of disintegrations of stationary measures 平稳测度分解的熵和维数

Transactions of the American Mathematical Society, Series B

Pub Date : 2019-08-05 DOI: 10.1090/BTRAN/60

Pablo Lessa

We extend a result of Ledrappier, Hochman, and Solomyak on exact dimensionality of stationary measures for SL 2 ( R ) text {SL}_2(mathbb {R}) to disintegrations of stationary measures for GL ⁡ ( R d ) operatorname {GL}(mathbb {R}^d) onto the one dimensional foliations of the space of flags obtained by forgetting a single subspace.

The dimensions of these conditional measures are expressed in terms of the gap between consecutive Lyapunov exponents, and a certain entropy associated to the group action on the one dimensional foliation they are defined on. It is shown that the entropies thus defined are also related to simplicity of the Lyapunov spectrum for the given measure on GL ⁡ ( R d ) operatorname {GL}(mathbb {R}^d) .

我们将Ledrappier, Hochman和Solomyak关于SL 2(R) text {SL}_2(mathbb {R})的平稳测度的精确维数的结果推广到GL (R d) operatorname {GL}(mathbb {R}^d)的平稳测度的分解到通过忽略单个子空间而得到的旗子空间的一维叶上。这些条件测度的维度用连续Lyapunov指数之间的间隙和与它们所定义的一维叶状上的群作用相关的一定熵来表示。结果表明，这样定义的熵也与给定测度GL (R d) operatorname {GL}(mathbb {R}^d)的李雅普诺夫谱的简单性有关。

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引用次数: 3

Characteristic-free test ideals 无特性测试理想

Transactions of the American Mathematical Society, Series B

Pub Date : 2019-07-03 DOI: 10.1090/btran/55

Felipe Pérez, Rebecca R.G.

Tight closure test ideals have been central to the classification of singularities in rings of characteristic p > 0 p>0 , and via reduction to characteristic p > 0 p>0 , in equal characteristic 0 as well. Their properties and applications have been described by Schwede and Tucker [Progress in commutative algebra 2, Walter de Gruyter, Berlin, 2012]. In this paper, we extend the notion of a test ideal to arbitrary closure operations, particularly those coming from big Cohen-Macaulay modules and algebras, and prove that it shares key properties of tight closure test ideals. Our main results show how these test ideals can be used to give a characteristic-free classification of singularities, including a few specific results on the mixed characteristic case. We also compute examples of these test ideals.

紧闭检验理想对于特征p>0 p>0环中的奇点分类，以及通过约简到特征p>0 p>0，在相同的特征0中也是如此。它们的性质和应用已经由Schwede和Tucker描述[交换代数的进展2,Walter de Gruyter，柏林，2012]。在本文中，我们将测试理想的概念推广到任意闭包运算，特别是那些来自大Cohen-Macaulay模和代数的闭包运算，并证明了它具有紧闭包测试理想的关键性质。我们的主要结果显示了如何使用这些测试理想来给出奇异点的无特征分类，包括一些关于混合特征情况的具体结果。我们还计算了这些测试理想的例子。

引用次数: 13

Three topological reducibilities for discontinuous functions 不连续函数的三种拓扑可约性

Transactions of the American Mathematical Society, Series B

Pub Date : 2019-06-18 DOI: 10.1090/btran/115

A. Day, R. Downey, L. Westrick

We define a family of three related reducibilities, $leq_T$, $leq_{tt}$ and $leq_m$, for arbitrary functions $f,g:Xrightarrowmathbb R$, where $X$ is a compact separable metric space. The $equiv_T$-equivalence classes mostly coincide with the proper Baire classes. We show that certain $alpha$-jump functions $j_alpha:2^omegarightarrow mathbb R$ are $leq_m$-minimal in their Baire class. Within the Baire 1 functions, we completely characterize the degree structure associated to $leq_{tt}$ and $leq_m$, finding an exact match to the $alpha$ hierarchy introduced by Bourgain and analyzed by Kechris and Louveau.

对于任意函数$f,g:Xrightarrowmathbb R$，我们定义了一个由三个相关的可约性组成的族，$leq_T$, $leq_{tt}$和$leq_m$，其中$X$是紧可分度量空间。$equiv_T$ -等价类大多与适当的Baire类一致。我们展示了某些$alpha$ -跳转函数$j_alpha:2^omegarightarrow mathbb R$在它们的Baire类中是$leq_m$ -最小的。在Baire 1函数中，我们完全描述了与$leq_{tt}$和$leq_m$相关的度结构，找到了与Bourgain引入并由Kechris和Louveau分析的$alpha$层次结构的精确匹配。

引用次数: 5

Transversals, duality, and irrational rotation 截线、对偶性和不合理旋转

Transactions of the American Mathematical Society, Series B

Pub Date : 2019-05-31 DOI: 10.1090/btran/54

Anna Duwenig, Heath Emerson

An early result of Noncommutative Geometry was Connes’ observation in the 1980’s that the Dirac-Dolbeault cycle for the 2 2 -torus T 2 mathbb {T}^2 , which induces a Poincaré self-duality for T 2 mathbb {T}^2 , can be ‘quantized’ to give a spectral triple and a K-homology class in K K 0 ( A θ ⊗ A θ , C ) mathrm {KK}_0(A_theta otimes A_theta , mathbb {C}) providing the co-unit for a Poincaré self-duality for the irrational rotation algebra A θ

非交换几何的一个早期成果是Connes在20世纪80年代的观察，即22 -圆环T 2的Dirac-Dolbeault循环 mathbb {t}^2，这引出了t2的庞卡罗自对偶 mathbb {t}^2，可以“量子化”得到K K 0 (a θ⊗a θ， C)中的谱三重和K同调类。 mathrm {kk}0(a)theta otimes a……theta ， mathbb {c})给出了无理数旋转代数a θ A＿的poincar自对偶的协单位theta 对于任意θ∈R∈Q theta in mathbb {r}setminus mathbb {q} ．然而，Connes的证明依赖于k理论计算，并没有为这种对偶的单位提供一个代表性的循环。由于这种表示在对偶的应用中是至关重要的，因此我们在本文中以无界形式提供这种循环。我们的方法是构造一个有限生成的射影模，对于任意非零整数b b mathcal {l}＿{b} / A θ⊗A θ A＿theta otimes a……theta 通过使用Muhly, Renault和Williams的一个截线化简论证，将其应用于沿斜率θ线的一对Kronecker叶 theta θ + b theta 加上b，利用这些流彼此横向的事实。然后我们计算Connes的对偶[L b] [mathcal {l}＿{b}]并证明我们得到了一个可逆的τ b∈K K 0 (A θ， A θ) tau ＿{b}in mathrm {kk}0(a)theta ……theta )，由Dirac-Schrödinger操作符的等变束表示。等变博特周期性的一个应用给出了描述这种“b - b -扭转”泛函性的一种高指标定理形式，这使得我们可以用kk理论中两个结构的组合来描述科恩斯对偶性的单位。这就产生了该单位的显式谱表示——一种用于非交换环面对角嵌入的“量子化Thom类”。

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引用次数: 2

Algebras defined by Lyndon words and Artin-Schelter regularity 由Lyndon词和Artin-Schelter正则定义的代数

Transactions of the American Mathematical Society, Series B

Pub Date : 2019-05-27 DOI: 10.1090/btran/89

T. Gateva-Ivanova

Let X = { x 1 , x 2 , ⋯ , x n } X= {x_1, x_2, cdots , x_n} be a finite alphabet, and let K K be a field. We study classes C ( X , W ) mathfrak {C}(X, W) of graded K K -algebras A = K ⟨ X ⟩ / I A = Klangle Xrangle / I , generated by

设X= {X 1, X 2，⋯，X n} X= {x_1, x_2， cdots, x_n}是一个有限字母，设K K是一个域。我们研究分级K K -代数A = K⟨X⟩/ I A = Klangle Xrangle / I的类C (X, W) mathfrak {C}(X, W)，由X X生成并具有固定的障碍物W W。首先，我们没有对ww施加限制，并研究了C (X, W) mathfrak {C} (X, W)中的代数具有多项式增长和有限全局维数d d的情况。接下来我们考虑一类代数C (X, W) mathfrak {C} (X, W)，它们的障碍集合W W是林登词的反链。核心问题是“当一类C (X, W) mathfrak {C} (X, W)包含Artin-Schelter正则代数时?”每个类C (X, W) mathfrak {C} (X, W)定义了一个Lyndon对(N,W) (N,W)，如果N N是有限的，它唯一地决定了全局维数g g dim a g g ，dimA和Gelfand-Kirillov维数g K dim a g K dimA，对于每个A∈C (X, W) A in mathfrak {C}(X, W)。我们用< ml:mat找到了一个组合条件

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引用次数: 3

What makes a complex a virtual resolution? 是什么使复合体成为虚拟分辨率?

Transactions of the American Mathematical Society, Series B

Pub Date : 2019-04-12 DOI: 10.1090/btran/91

Michael C. Loper

Virtual resolutions are homological representations of finitely generated Pic ( X ) text {Pic}(X) -graded modules over the Cox ring of a smooth projective toric variety. In this paper, we identify two algebraic conditions that characterize when a chain complex of graded free modules over the Cox ring is a virtual resolution. We then turn our attention to the saturation of Fitting ideals by the irrelevant ideal of the Cox ring and prove some results that mirror the classical theory of Fitting ideals for Noetherian rings.

虚分辨率是光滑射影环的Cox环上有限生成的Pic (X) text {Pic}(X) -梯度模的同调表示。在本文中，我们确定了两个代数条件，表征了Cox环上的分级自由模链复形是虚分辨率。然后，我们将注意力转向Cox环的不相关理想对拟合理想的饱和，并证明了一些反映Noetherian环拟合理想经典理论的结果。

引用次数: 11

Kronecker positivity and 2-modular representation theory Kronecker正性与2模表示理论

Transactions of the American Mathematical Society, Series B

Pub Date : 2019-03-18 DOI: 10.1090/btran/70

C. Bessenrodt, C. Bowman, L. Sutton

This paper consists of two prongs. Firstly, we prove that any Specht module labelled by a 2-separated partition is semisimple and we completely determine its decomposition as a direct sum of graded simple modules. Secondly, we apply these results and other modular representation theoretic techniques on the study of Kronecker coefficients and hence verify Saxl’s conjecture for several large new families of partitions. In particular, we verify Saxl’s conjecture for all irreducible characters of S n mathfrak {S}_n which are of 2-height zero.

这篇论文由两部分组成。首先，我们证明了任何被2分割的划分标记的Specht模块都是半简单的，并完全确定了它的分解为分级简单模块的直接和。其次，我们将这些结果和其他模表示理论技术应用于Kronecker系数的研究，从而验证了Saxl猜想对于几个新的大划分族。特别地，我们验证了Saxl的猜想对于S n mathfrak {S}_n中所有2-高度为零的不可约字符。

引用次数: 9

Kernel theorems in coorbit theory 共轨理论中的核定理

Transactions of the American Mathematical Society, Series B

Pub Date : 2019-03-07 DOI: 10.1090/BTRAN/42

P. Balázs, K. Grōchenig, M. Speckbacher

We prove general kernel theorems for operators acting between coorbit spaces. These are Banach spaces associated to an integrable representation of a locally compact group and contain most of the usual function spaces (Besov spaces, modulation spaces, etc.). A kernel theorem describes the form of every bounded operator between a coorbit space of test functions and distributions by means of a kernel in a coorbit space associated to the tensor product representation. As special cases we recover Feichtinger’s kernel theorem for modulation spaces and the recent generalizations by Cordero and Nicola. We also obtain a kernel theorem for operators between the Besov spaces B ˙ 1 , 1 0 dot {B}^0_{1,1} and B ˙ ∞ , ∞ 0 dot {B}^{0}_{infty , infty } .

我们证明了作用于共轨空间之间的算子的一般核定理。这些是与局部紧群的可积表示相关的Banach空间，并且包含了大多数常用的函数空间(Besov空间，调制空间等)。核定理通过与张量积表示相关联的共轨空间中的核，描述了在测试函数和分布的共轨空间之间的每一个有界算子的形式。作为特例，我们恢复了调制空间的Feichtinger核定理和Cordero和Nicola最近的推广。我们还得到了Besov空间B˙1,10 dot B^0＿1,{1和}B{˙∞}，∞0 dot B{^}0＿{}{infty, infty之间算子的核定理}。

引用次数: 15

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