Chiral de Rham Complex and Orbifolds

Details Chiral de Rham Complex and Orbifolds Chiral de Rham Complex and Orbifolds

2003-07-14

arxiv.org/abs/math/0307181v2

Mathematics

Algebraic Geometry

Scientific paper

Suppose that a finite group $G$ acts on a smooth complex variety $X$. Then this action lifts to the Chiral de Rham Complex of $X$ and to its cohomology by automorphisms of the vertex algebra structure. We define twisted sectors for the Chiral de Rham Complex (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.

Affiliated with

Also associated with

No associations

Rating

Chiral de Rham Complex and Orbifolds does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Chiral de Rham Complex and Orbifolds, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Chiral de Rham Complex and Orbifolds will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-381978