@article {2011,
	title = {Poincar{\'e} polynomial of moduli spaces of framed sheaves on (stacky) Hirzebruch surfaces},
	journal = {Communications in Mathematical Physics 304 (2011) 395-409},
	volume = {304},
	number = {SISSA;56/2009/FM},
	year = {2011},
	month = {06/2011},
	pages = {395-409},
	publisher = {Springer},
	abstract = {<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>},
	doi = {10.1007/s00220-011-1231-z},
	url = {http://hdl.handle.net/1963/3738},
	author = {Ugo Bruzzo and Rubik Poghossian and Alessandro Tanzini}
}
@article {2010,
	title = {Picard group of hypersurfaces in toric varieties},
	number = {SISSA;78/2010/FM},
	year = {2010},
	abstract = {We show that the usual sufficient criterion for a generic hypersurface in a smooth projective manifold to have the same Picard number as the ambient variety can be generalized to hypersurfaces in complete simplicial toric varieties. This sufficient condition is always satisfied by generic K3 surfaces embedded in Fano toric 3-folds.},
	url = {http://hdl.handle.net/1963/4103},
	author = {Ugo Bruzzo and Antonella Grassi}
}
