# Twisted genera of symmetric products

@article{Maxim2009TwistedGO,
title={Twisted genera of symmetric products},
author={Laurenţiu Maxim and J{\"o}rg Sch{\"u}rmann},
journal={Selecta Mathematica},
year={2009},
volume={18},
pages={283-317}
}
• Published 6 June 2009
• Mathematics
• Selecta Mathematica
We give a new proof of formulae for the generating series of (Hodge) genera of symmetric products X(n) with coefficients, which hold for complex quasi-projective varieties X with any kind of singularities and which include many of the classical results in the literature as special cases. Important specializations of our results include generating series for extensions of Hodge numbers and Hirzebruch’s χy-genus to the singular setting and, in particular, generating series for intersection…
Cohomology representations of external and symmetric products of varieties
• Mathematics
• 2016
We prove refined generating series formulae for characters of (virtual) cohomology representations of external products of suitable coefficients on (possibly singular) complex quasi-projective
Characteristic classes of symmetric products of complex quasi-projective varieties
• Mathematics
• 2010
We prove generating series formulae for suitable twisted characteristic classes of symmetric products of a singular complex quasi-projective variety. More concretely, we study homology Hirzebruch
Equivariant Hodge-Deligne polynomials of symmetric products of algebraic groups
Let $X$ be a complex quasi-projective algebraic variety. In this paper we study the mixed Hodge structures of the symmetric products $Sym^{n}X$ when the cohomology of $X$ is given by exterior
Intersection cohomology of moduli spaces of vector bundles over curves
• Mathematics
• 2015
We compute the intersection cohomology of the moduli spaces $M(r,d)$ of semistable vector bundles of arbitrary rank $r$ and degree $d$ over a curve. To do this, we introduce new invariants, called
Equivariant Characteristic Classes of Singular Complex Algebraic Varieties
• Mathematics
• 2012
Homology Hirzebruch characteristic classes for singular varieties have been recently defined by Brasselet, Schüurmann, and Yokura as an attempt to unify previously known characteristic class theories
Equivariant characteristic classes of external and symmetric products of varieties
• Mathematics
• 2015
We obtain refined generating series formulae for equivariant characteristic classes of external and symmetric products of singular complex quasi-projective varieties. More concretely, we study
Discriminants in the Grothendieck Ring
• Mathematics
• 2015
We consider the "limiting behavior" of *discriminants*, by which we mean informally the locus in some parameter space of some type of object where the objects have certain singularities. We focus on
Characteristic classes and Hilbert-Poincar\'e series for perverse sheaves on abelian varieties
Abstract. The convolution powers of a perverse sheaf on an abelian variety define an interesting family of branched local systems whose geometry is still poorly understood. We show that the

## References

SHOWING 1-10 OF 68 REFERENCES
Characteristic classes of symmetric products of complex quasi-projective varieties
• Mathematics
• 2010
We prove generating series formulae for suitable twisted characteristic classes of symmetric products of a singular complex quasi-projective variety. More concretely, we study homology Hirzebruch
Mixed Hodge polynomials of character varieties
• Mathematics
• 2006
We calculate the E-polynomials of certain twisted GL(n,ℂ)-character varieties $\mathcal{M}_{n}$ of Riemann surfaces by counting points over finite fields using the character table of the finite group
Equivariant Genera of Complex Algebraic Varieties
• Mathematics
• 2009
For smooth manifolds, Atiyah and Meyer studied contributions of monodromy to usual signatures. In this note we obtain Atiyah-Meyer type formulae for equivariant Hodge-theoretic genera of complex
Resolving mixed Hodge modules on configuration spaces
Given a mixed Hodge module E on a scheme X over the complex numbers, and a quasi-projective morphism f:X->S, we construct in this paper a natural resolution of the nth exterior tensor power of E
Hirzebruch classes and motivic Chern classes for singular (complex) algebraic varieties
• Mathematics
• 2004
In this paper we study some new theories of characteristic homology classes for singular complex algebraic varieties. First we introduce a natural transformation T_{y}: K_{0}(var/X) -> H_{*}(X,Q)[y]
Generating functions of orbifold Chern classes I: symmetric products
• T. Ohmoto
• Mathematics
Mathematical Proceedings of the Cambridge Philosophical Society
• 2008
Abstract In this paper, for a possibly singular complex variety X, generating functions of total orbifold Chern homology classes of the symmetric products SnX are given. These are very natural “class
HIRZEBRUCH CLASSES AND MOTIVIC CHERN CLASSES FOR SINGULAR SPACES
• Mathematics
• 2005
In this paper we study some new theories of characteristic homology classes of singular complex algebraic (or compactifiable analytic) spaces. We introduce a motivic Chern class transformationmCy:
The elliptic curve in the S-duality theory and Eisenstein series for Kac-Moody groups
We establish a relation between the generating functions appearing in the S-duality conjecture of Vafa and Witten and geometric Eisenstein series for Kac-Moody groups. For a pair consisting of a