Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911

   
 

 

Chiral de Rham complex and orbifolds


Authors: Edward Frenkel and Matthew Szczesny
Journal: J. Algebraic Geom. 16 (2007), 599-624
DOI: https://doi.org/10.1090/S1056-3911-07-00466-3
Published electronically: May 1, 2007
MathSciNet review: 2357685
Full-text PDF

Abstract | References | Additional Information

Abstract: Suppose that a finite group $ G$ acts on a smooth complex variety $ X$. Then this action lifts to the Chiral de Rham complex $ \Omega^{\operatorname{ch}}_{X}$ of $ X$ and to its cohomology by automorphisms of the vertex algebra structure. We define twisted sectors for $ \Omega^{\operatorname{ch}}_{X}$ (and their cohomologies) as sheaves of twisted vertex algebra modules supported on the components of the fixed-point sets $ X^{g}, g \in G$. Each twisted sector sheaf carries a BRST differential and is quasi-isomorphic to the de Rham complex of $ X^{g}$. Putting the twisted sectors together with the vacuum sector and taking $ G$-invariants, we recover the additive and graded structures of Chen-Ruan orbifold cohomology. Finally, we show that the orbifold elliptic genus is the partition function of the direct sum of the cohomologies of the twisted sectors.


References [Enhancements On Off] (What's this?)


Additional Information

Edward Frenkel
Affiliation: Department of Mathematics, University of California, Berkeley, California 94720
Email: frenkel@math.berkeley.edu

Matthew Szczesny
Affiliation: Department of Mathematics, Boston University, 111 Cummington Street, Boston, Massachusetts 02215
Email: szczesny@math.upenn.edu

DOI: https://doi.org/10.1090/S1056-3911-07-00466-3
Received by editor(s): January 1, 2004
Received by editor(s) in revised form: November 6, 2006
Published electronically: May 1, 2007
Additional Notes: The first author was partially supported by grants from the Packard Foundation and the NSF

Journal of Algebraic Geometry
The Journal of Algebraic Geometry
is sponsored by the Department of Mathematical Sciences
of Tsinghua University
and is distributed by the American Mathematical Society
for University Press, Inc.
Online ISSN 1534-7486; Print ISSN 1056-3911
© 2017 University Press, Inc.
Comments: jag-query@ams.org
AMS Website