Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userAbelian Hurwitz-Hodge integrals
111
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
Hodge classes on the moduli space of admissible covers with monodromy group G are associated to irreducible representations of G. We evaluate all linear Hodge integrals over moduli spaces of admissible covers with abelian monodromy in terms of multiplication in an associated wreath group algebra. In case G is cyclic and the representation is faithful, the evaluation is in terms of double Hurwitz numbers. In case G is trivial, the formula specializes to the well-known result of Ekedahl-Lando-Shapiro-Vainshtein for linear Hodge integrals over the moduli space of curves in terms of single Hurwitz numbers.
rate research
Read More
We start with a curve over an algebraically closed ground field of positive characteristic $p>0$. By using specialization techniques, under suitable natural coprimality conditions, we prove a cohomological Simpson Correspondence between the moduli space of Higgs bundles and the one of connections on the curve. We also prove a new $p$-multiplicative periodicity concerning the cohomology rings of Dolbeault moduli spaces of degrees differing by a factor of $p$. By coupling this $p$-periodicity in characteristic $p$ with lifting/specialization techniques in mixed characteristic, we find, in arbitrary characteristic, cohomology ring isomorphisms between the cohomology rings of Dolbeault moduli spaces for different degrees coprime to the rank. It is interesting that this last result is proved as follows: we prove a weaker version in positive characteristic; we lift and strengthen the weaker version to the result in characteristic zero; finally, we specialize the result to positive characteristic. The moduli spaces we work with admit certain natural morphisms (Hitchin, de Rham-Hitchin, Hodge-Hitchin), and all the cohomology ring isomorphisms we find are filtered isomorphisms for the resulting perverse Leray filtrations.
In this paper, we show that the generating function for linear Hodge integrals over moduli spaces of stable maps to a nonsingular projective variety $X$ can be connected to the generating function for Gromov-Witten invariants of $X$ by a series of differential operators ${ L_m mid m geq 1 }$ after a suitable change of variables. These operators satisfy the Virasoro bracket relation and can be seen as a generalization of the Virasoro operators appeared in the Virasoro constraints for Kontsevich-Witten tau-function in the point case. This result is an extension of the work in cite{LW} for the point case which solved a conjecture of Alexandrov.
We describe a sequence of effective divisors on the Hurwitz space $H_{d,g}$ for $d$ dividing $g-1$ and compute their cycle classes on a partial compactification. These divisors arise from vector bundles of syzygies canonically associated to a branched cover. We find that the cycle classes are all proportional to each other.
Hurwitz spaces parameterizing covers of the Riemann sphere can be equipped with a Frobenius structure. In this review, we recall the construction of such Hurwitz Frobenius manifolds as well as the correspondence between semisimple Frobenius manifolds and the topological recursion formalism. We then apply this correspondence to Hurwitz Frobenius manifolds by explaining that the corresponding primary invariants can be obtained as periods of multidifferentials globally defined on a compact Riemann surface by topological recursion. Finally, we use this construction to reply to the following question in a large class of cases: given a compact Riemann surface, what does the topological recursion compute?
In this paper we study the reduction of Galois covers of curves, from characteristic 0 to characteristic p. The starting point is a is a recent result of Raynaud which gives a criterion for good reduction for covers of the projective line branch at 3 points. Under some condition on the Galois group, we extend this criterion to the case of 4 branch points. Moreover, we describe the reduction of the Hurwitz space of such covers and compute the number of covers with good reduction.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
