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BPS invariants of semi-stable sheaves on rational surfaces

Mathematical Physics 2013-06-11 v3 High Energy Physics - Theory Algebraic Geometry math.MP

Abstract

BPS invariants are computed, capturing topological invariants of moduli spaces of semi-stable sheaves on rational surfaces. For a suitable stability condition, it is proposed that the generating function of BPS invariants of a Hirzebruch surface takes the form of a product formula. BPS invariants for other stability conditions and other rational surfaces are obtained using Harder-Narasimhan filtrations and the blow-up formula. Explicit expressions are given for rank <4 sheaves on a Hirzebruch surface or the projective plane. The applied techniques can be applied iteratively to compute invariants for higher rank.

Keywords

Cite

@article{arxiv.1109.4861,
  title  = {BPS invariants of semi-stable sheaves on rational surfaces},
  author = {Jan Manschot},
  journal= {arXiv preprint arXiv:1109.4861},
  year   = {2013}
}

Comments

26 pages, version submitted to journal