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/1963/373800891nas a2200121   4500008004300000245004600043210004600089520053600135100001600671700002200687700002400709856003600733       2008                        en_Ud  00aInstanton counting on Hirzebruch surfaces0 aInstanton counting on Hirzebruch surfaces3 aWe perform a study of the moduli space of framed torsion free sheaves on Hirzebruch surfaces by using localization techniques. After discussing general properties of this moduli space, we classify its fixed points under the appropriate toric action and compute its Poincare\\\' polynomial. From the physical viewpoint, our results provide the partition function of N=4 Vafa-Witten theory on Hirzebruch surfaces, which is relevant in black hole entropy counting problems according to a conjecture due to Ooguri, Strominger and Vafa.1 aBruzzo, Ugo1 aPoghossian, Rubik1 aTanzini, Alessandro  uhttp://hdl.handle.net/1963/285200790nas a2200133   4500008004300000245005400043210005200097520038200149100002200531700002100553700002200574700002400596856003600620       2006                        en_Ud  00aN=1 superpotentials from multi-instanton calculus0 aN1 superpotentials from multiinstanton calculus3 aIn this paper we compute gaugino and scalar condensates in N = 1 supersymmetric gauge\\ntheories with and without massive adjoint matter, using localization formulae over the multi-instanton moduli space. Furthermore we compute the chiral ring relations among the correlators of the N = 1* theory and check this result against the multi-instanton computation finding agreement.1 aFucito, Francesco1 aMorales, Jose F.1 aPoghossian, Rubik1 aTanzini, Alessandro  uhttp://hdl.handle.net/1963/1773