BPS invariants of semi-stable sheaves on rational surfaces

Details BPS invariants of semi-stable sheaves on rational surfaces BPS invariants of semi-stable sheaves on rational surfaces

2011-09-22

arxiv.org/abs/1109.4861v2

Physics

Mathematical Physics

23 pages

Scientific paper

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.

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