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.

%B Communications in Mathematical Physics 304 (2011) 395-409 %I Springer %V 304 %P 395-409 %8 06/2011 %G en_US %U http://hdl.handle.net/1963/3738 %N 2 %1 579 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-09-09T09:26:43Z\\r\\nNo. of bitstreams: 1\\r\\nBPT-8.pdf: 250954 bytes, checksum: 984c30f0144339468a97f54d6b22ce05 (MD5) %R 10.1007/s00220-011-1231-z %0 Report %D 2008 %T Instanton counting on Hirzebruch surfaces %A Ugo Bruzzo %A Rubik Poghossian %A Alessandro Tanzini %X We 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. %G en_US %U http://hdl.handle.net/1963/2852 %1 1848 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-09-05T18:06:43Z\\nNo. of bitstreams: 1\\n0809.0155v1.pdf: 212427 bytes, checksum: f5060bd4e1da6a5215a488041ef018ff (MD5) %0 Report %D 2006 %T N=1 superpotentials from multi-instanton calculus %A Francesco Fucito %A Jose F. Morales %A Rubik Poghossian %A Alessandro Tanzini %X In 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. %B JHEP01(2006)031 %G en_US %U http://hdl.handle.net/1963/1773 %1 2771 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2006-03-29T07:58:23Z\\nNo. of bitstreams: 1\\n73FM-2005.pdf: 325303 bytes, checksum: 89f205e907378d543e7a51042f437c8a (MD5) %R 10.1088/1126-6708/2006/01/031