Abstract
Bogomolnyi-Prasad-Sommerfield (BPS) invariants are computed, capturing topo- logical invariants of moduli spaces of semi-stable sheaves on rational surfaces. For a suit- able 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 fil- trations and the blow-up formula. Explicit expressions are given for rank ≤3 sheaves on � � and the projective plane P 2 . The applied techniques can be applied iteratively to com- pute invariants for higher rank.
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