2006/03/21 by Toru Sasaki, Sasaki, Toru · 3 citations
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #hep-th #math.AG
paper · pdf · doi:10.48550/arxiv.hep-th/0603162
31 pages, reference and appendix added
arxiv created 2006/05/16 · arxiv updated 2009/12/01
We calculate Betti numbers of the framed moduli space of instantons on \bf C2/\bf Z2, under the assumption that the corresponding torsion free sheaves E have vanishing properties (Hom(E,E(-l_∞))=Ext2(E,E(-l_∞))=0). Moreover we derive the generating function of Betti numbers and obtain closed formulas. On the other hand, we derive a universal relation between the generating function of Betti numbers of the moduli spaces of stable sheaves on X with an A1-singularity and that on X blow-uped at the singularity, by using Weil conjecture. We call this the O(-2) blow-up formula. Applying this to X=\bf C2/\bf Z2 case, we reproduce the formula given by instanton calculus.