Communications in Mathematical Physics

, Volume 304, Issue 2, pp 395–409 | Cite as

Poincaré Polynomial of Moduli Spaces of Framed Sheaves on (Stacky) Hirzebruch Surfaces

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Abstract

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 Poincaré 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 mathematical framework for the counting of D4-D2-D0 branes bound states on total spaces of the bundles \({\mathcal {O}_{\mathbb {P}^1}(-p)}\) .

Keywords

Black Hole Gauge Theory Modulus Space Line Bundle Topological String 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  • Ugo Bruzzo
    • 1
    • 2
  • Rubik Poghossian
    • 3
    • 4
  • Alessandro Tanzini
    • 1
    • 2
  1. 1.Scuola Internazionale Superiore di Studi AvanzatiTriesteItalia
  2. 2.Istituto Nazionale di Fisica NucleareSezione di TriesteTriesteItalia
  3. 3.Istituto Nazionale di Fisica NucleareSezione di Roma Tor VergataRomaItalia
  4. 4.Yerevan Physics InstituteYerevanArmenia

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