The equivariant Euler characteristic of moduli spaces of curves

We give a formula for the S_n - equivariant Euler characteristics of the moduli spaces of genus g curves with n marked pointsComment: 7 pages; v3: references and bibliography corrected to match the published versio

On the motivic measure on the space of functions

Motivic measure on the space of functions was introduced by Campillo, Delgado and Gusein-Zade as an analog of the motivic measure on the space of arcs . In this paper we prove that the measure on the space of functions can be related to the motivic measure on the space of arcs by a factor, which can be defined explicitly in geometric terms. This provides a possibility to rewrite motivic integrals over the space of functions as integrals over the union of all symmetric powers of the space of arcs.Comment: 13 page

Infinitesimal change of stable basis

The purpose of this note is to study the Maulik–Okounkov K-theoretic stable basis for the Hilbert scheme of points on the plane, which depends on a “slope” m∈ R. When m=ab is rational, we study the change of stable matrix from slope m- ε to m+ ε for small ε> 0 , and conjecture that it is related to the Leclerc–Thibon conjugation in the q-Fock space for Uqgl^ b. This is part of a wide framework of connections involving derived categories of quantized Hilbert schemes, modules for rational Cherednik algebras and Hecke algebras at roots of unity

Compactified Jacobians and q,t-Catalan Numbers, I

J. Piontkowski described the homology of the Jacobi factor of a plane curve singularity with one Puiseux pair. We discuss the combinatorial structure of his answer, in particular, relate it to the bigraded deformation of Catalan numbers introduced by A. Garsia and M. Haiman.Comment: Revised version, 24 page