来自与不动点对应的Prym-Tyurin簇

Prym-Tyurin品种的分化类型

Polarization types of isogenous Prym-Tyurin varieties

设p：C-->Y是光滑射影曲线的覆盖，它是2次π：C-->C'和n次g：C'-->Y的合成.设f：X-->Y是2 ^n次覆盖，其中曲线X表示g：C '-->Y的纤维在C^{（n）}中的提升.设P（X，δ）是相伴的Prym-Tyurin簇，已知它与Prym簇P（C，C '）同源.本文的大部分结果集中于计算JX正则极化对P（X，δ）的限制的极化类型。我们得到了n=3时的极化类型。当Y=P^1时，我们猜想P（X，δ）同构于Prym簇P（C，C '）的对偶.当n=2时这是已知的，当n=3时我们证明它，并且对于任意的n，如果π：C-->C'是tale。对于一些其他类型的覆盖也得到了类似的结果。

$\mathcal{A}_6$上Prym-Tyurin构造的最优性

Optimality of the Prym-Tyurin construction for $\mathcal{A}_6$

本文证明在非常一般的principally polarized abelian 6-折线上，最小曲线类的最小倍数由代数循环表示为6。

Tau functions, Prym-Tyurin classes and loci of degenerate differentials

We study the rational Picard group of the projectivized moduli space of holomorphic n-differentials on complex genus g stable curves. We define (n - 1) natural classes in this Picard group that we call Prym-Tyurin classes. We express these classes as linear combinations of boundary divisors and the divisor of n-differentials with a double zero. We give two different proofs of this result, using two alternative approaches: an analytic approach that involves the Bergman tau function and its vanishing divisor and an algebro-geometric approach that involves cohomological computations on the univer…

图的Prym簇

Prym varieties associated to graphs

我们提出了一个Prym构造，它将阿贝尔簇与点传递强正则图联系起来。作为应用，我们构造了任意指数$\geq 3$的Prym-Tyurin簇，推广了Lange，Recillas和Rochas的一个结果.

The uniformization of the moduli space of principally polarized abelian 6-folds

Starting from a beautiful idea of Kanev, we construct a uniformization of the moduli space A_6 of principally polarized abelian 6-folds in terms of curves and monodromy data. We show that the general ppav of dimension 6 is a Prym-Tyurin variety corresponding to a degree 27 cover of the projective line having monodromy the Weyl group of the E_6 lattice. Along the way, we establish numerous facts concerning the geometry of the Hurwitz space of such E_6-covers, including: (1) a proof that the canonical class of the Hurwitz space is big, (2) a concrete geometric description of the Hodge-Hurwitz ei…

覆盖对的Prym簇的极化

Polarizations of Prym Varieties of pairs of coverings

对于光滑射影曲线的任何一对覆盖$f_i: X \ra X_i, i = 1,2$，人们可以将雅可比$J_X$的交换子簇，对$(f_1,f_2)$的Prym簇$P(f_1,f_2)$联系起来。在某些情况下，我们可以计算$JX$的正则主极化的限制类型。得到了2个指数为6的Prym-Tyurin簇。

A pointed Prym-Petri Theorem

We construct pointed Prym-Brill-Noether varieties parametrizing line bundles assigned to an irreducible étale double covering of a curve with a prescribed minimal vanishing at a fixed point. We realize them as degeneracy loci in type D and deduce their classes in case of expected dimension. Thus, we determine a pointed Prym-Petri map and prove a pointed version of the Prym-Petri theorem implying that the expected dimension holds in the general case. These results build on work of Welters and De Concini-Pragacz on the unpointed case. Finally, we show that Prym varieties are Prym-Tyurin varietie…

外尔群的Prym簇的阿贝尔化

Polarizations of Prym varieties for Weyl groups via abelianization

设$π: Z \ra X$是光滑射影曲线的Galois覆盖，其Galois群是单连通李群$G$的Weyl群.对于任何主导权重$λ$，考虑曲线$Y = Z/\Stab(λ)$。Kanev对应定义了$Y$的雅可比矩阵的一个阿贝尔子簇$P_λ$。在某些情况下，我们计算了$\Jac(Y)$的正则主极化限制到$P_λ$的极化类型.特别地，在组$E_8$的情况下，我们获得了Prym-Tyurin变种的家族。主要思想是利用Donagi-Prym簇的阿贝尔化映射到曲线$X$上的主$G$ -丛的模栈。

W(E_6)-覆盖的模空间上的 Hodge 类与 A_6 的几何

Hodge classes on the moduli space of W(E_6)-covers and the geometry of A_6

本文确定 W(E_6)-覆盖 Hurwitz 空间上对应 Weyl 群25个不可约表示的 Hodge 类，并给出 A_6 经 W(E_6) 型 Prym-Tyurin 簇单值化的初等证明。