Related papers: Abelian Hurwitz-Hodge integrals

We provide a formula describing the G-module structure of the Hurwitz-Hodge bundle for admissible G-covers in terms of the Hodge bundle of the base curve, and more generally, for describing the G-module structure of the push-forward to the…

Ekedahl, Lando, Shapiro, and Vainshtein announced a remarkable formula expressing Hurwitz numbers (counting covers of the projective line with specified simple branch points, and specified branching over one other point) in terms of Hodge…

We compute the degree of Hurwitz-Hodge classes $\lambda_1^e$ on one dimensional moduli spaces of cyclic admissible covers of the projective line. We also compute the degree of the the first Chern class of the Hodge bundle $\lambda_1$ for…

Let $K$ be an algebraically closed field of characteristic zero, and let $G$ be a connected reductive algebraic group over $K$. We address the problem of classifying triples $(G,H,V)$, where $H$ is a proper connected subgroup of $G$, and…

Moduli spaces of admissible covers and stable maps of target curves give rise to cycles on $\overline{M}_{g,n}$. We prove a formula relating these cycles. It recovers both the Ekedahl-Lando-Shapiro-Vainshtein formula and the…

We establish relations between representation dimensions of two algebras connected by a Frobenius bimodule or extension. Consequently, upper bounds and equality formulas for representation dimensions of group algebras, symmetric separably…

For any finite abelian group G, we study the moduli space of abelian $G$-covers of elliptic curves, in particular identifying the irreducible components of the moduli space. We prove that, in the totally ramified case, the moduli space has…

We compute the subgroup of the monodromy group of a generalized Kummer variety associated to equivalences of derived categories of abelian surfaces. The result was previously announced in arXiv:1201.0031. Mongardi showed that the subgroup…

In this paper we study certain category of smooth modules for reductive $p$--adic groups analogous to the usual smooth complex representations but with the field of complex numbers replaced by a $\mathbb Q$--algebra. We prove some…

It is one of the wonderful ``coincidences'' of the theory of finite groups that the simple group G of order 25920 arises as both a symplectic group in characteristic 3 and a unitary group in characteristic 2. These two realizations of G…

We consider components of Hurwitz moduli space of G-Galois covers and set up a powerful algebraic framework to study the set of corresponding equivalence classes of monodromy maps. Within that we study geometric stabilisation by various…

We study Hodge Integrals on Moduli Spaces of Admissible Covers. Motivation for this work comes from Bryan and Pandharipande's recent work on the local GW theory of curves, where analogouos intersection numbers, computed on Moduli Spaces of…

We prove that the moduli spaces A_3(D) of polarized abelian threefolds with polarizations of types D=(1,1,2), (1,2,2), (1,1,3) or (1,3,3) are unirational. The result is based on the study of families of simple coverings of elliptic curves…

Let $G$ be a simple linear algebraic group over an algebraically closed field $K$ of characteristic $p \geqslant 0$, let $H$ be a proper closed subgroup of $G$ and let $V$ be a nontrivial finite dimensional irreducible rational $KG$-module.…

In this paper we describe explicit generating functions for a large class of Hurwitz-Hodge integrals. These are integrals of tautological classes on moduli spaces of admissible covers, a (stackily) smooth compactification of the Hurwitz…

Let $G$ be a connected reductive group defined and split over a non-archimedean local field $F$. We give a new geometric proof of a special case of a recent theorem of Solleveld. Namely, we show that the class of standard Iwahori-spherical…

Using Atiyah-Bott localization on the space of stable maps to the stack quotient $[\mathbb{P}^1/\mathbb{Z}_2]$, we find recursions that determine all Hodge integrals with descendent insertions at one marked point on the hyperelliptic locus…

An algebraic classification is given for spaces of holomorphic vector-valued modular forms of arbitrary real weight and multiplier system, associated to irreducible, T-unitarizable representations of the full modular group, of dimension…

Let $\mathbb{F}$ be an algebraically closed field and $G$ be an almost quasi-simple group. An important problem in representation theory is to classify the subgroups $H<G$ and $\mathbb{F} G$-modules $L$ such that the restriction…

We prove the integral Hodge conjecture for one-cycles on a principally polarized complex abelian variety whose minimal class is algebraic. In particular, any product of Jacobians of smooth projective curves over the complex numbers…