709 research outputs found
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 MaulikāOkounkov K-theoretic stable basis for the Hilbert scheme of points on the plane, which depends on a āslopeā mā R. When m=ab is rational, we study the change of stable matrix from slope m- Īµ to m+ Īµ for small Īµ> 0 , and conjecture that it is related to the LeclercāThibon 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
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