01388nas a2200157   4500008004300000245009200043210007000135260002200205300001200227490000800239520088500247100001601132700002201148700002401170856003601194       2011                        en_Ud  00aPoincaré polynomial of moduli spaces of framed sheaves on (stacky) Hirzebruch surfaces0 aPoincaré polynomial of moduli spaces of framed sheaves on stacky  bSpringerc06/2011  a395-4090 v3043 a<p>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.</p>1 aBruzzo, Ugo1 aPoghossian, Rubik1 aTanzini, Alessandro  uhttp://hdl.handle.net/1963/3738