On the Sn-equivariant Euler characteristic of moduli spaces of hyperelliptic curves
نویسنده
چکیده
The generating function for Sn-equivariant Euler characteristics of moduli spaces of pointed hyperelliptic curves for any genus g ≥ 2 is calculated. This answer generalizes the known ones for genera 2 and 3 and answers obtained by J. Bergstrom for any genus and n ≤ 7 points.
منابع مشابه
The equivariant Euler characteristic of moduli spaces of curves.
We give a formula for the Sn-equivariant Euler characteristics of the moduli spaces Mg,n of genus g curves with n marked points.
متن کاملEquivariant Counts of Points of the Moduli Spaces of Pointed Hyperelliptic Curves
Abstract. In this article we consider the moduli space Hg,n of n-pointed smooth hyperelliptic curves of genus g. In order to get cohomological information we wish to make Sn-equivariant counts of the numbers of points defined over finite fields of this moduli space. We find that there are recursion formulas in the genus that these numbers fulfill. Thus, if we can make Sn-equivariant counts of H...
متن کاملCohomology of Moduli Spaces of Curves of Genus Three via Point Counts
In this article we consider the moduli space of smooth n-pointed nonhyperelliptic curves of genus three. In the pursuit of cohomological information about this space, we make Sn-equivariant counts of its numbers of points defined over finite fields for n up to seven. Together with results on the moduli spaces of smooth pointed curves of genus zero, one and two, and the moduli space of smooth hy...
متن کاملThe Euler Characteristic of Local Systems on the Moduli of Genus 3 Hyperelliptic Curves
For a partition λ = {λ1 ≥ λ2 ≥ λ3 ≥ 0} of non-negative integers, we calculate the Euler characteristic of the local system Vλ on the moduli space of genus 3 hyperelliptic curves using a suitable stratification. For some λ of low degree, we make a guess for the motivic Euler characteristic of Vλ using counting curves over finite fields.
متن کاملPermutation - Equivariant Quantum K - Theory
K-theoretic Gromov-Witten (GW) invariants of a complex algebraic manifold X are defined as super-dimensions of sheaf cohomology of interesting bundles over moduli spaces of n-pointed holomorphic curves in X. In this paper, we introduce K-theoretic GW-invariants cognizant of the Sn-module structure on the sheaf cohomology, induced by renumbering of the marked points, and compute such invariants ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008