Poincare polynomial of moduli spaces of framed sheaves on (stacky) Hirzebruch surfaces

Details Poincare polynomial of moduli spaces of framed sheaves on (stacky) Hirzebruch surfaces Poincare polynomial of moduli spaces of framed sheaves on (stacky) Hirzebruch surfaces

2009-09-08

arxiv.org/abs/0909.1458v2

Commun.Math.Phys.304:395-409,2011

Mathematics

Algebraic Geometry

17 pages. This submission supersedes arXiv:0809.0155 [math.AG]

Scientific paper

10.1007/s00220-011-1231-z

We perform a study of the moduli space of framed torsion-free sheaves on Hirzebruch surfaces by using localization techniques. We discuss some general properties of this moduli space by studying it in the framework of Huybrechts-Lehn theory of framed modules. We classify the fixed points under a toric action on the moduli space, and use this to compute the Poincare polynomial of the latter. This will imply that the moduli spaces we are considering are irreducible. We also consider fractional first Chern classes, which means that we are extending our computation to a stacky deformation of a Hirzebruch surface. From the physical viewpoint, our results provide the partition function of N=4 Vafa-Witten theory on total spaces of line bundles on P1, which is relevant in black hole entropy counting problems according to a conjecture due to Ooguri, Strominger and Vafa.

Affiliated with

Also associated with

No associations

Rating

Poincare polynomial of moduli spaces of framed sheaves on (stacky) Hirzebruch surfaces 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 Poincare polynomial of moduli spaces of framed sheaves on (stacky) Hirzebruch surfaces, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Poincare polynomial of moduli spaces of framed sheaves on (stacky) Hirzebruch surfaces will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-108276