Bogomolov-Gieseker type inequality and counting invariants

Details Bogomolov-Gieseker type inequality and counting invariants Bogomolov-Gieseker type inequality and counting invariants

2011-12-15

arxiv.org/abs/1112.3411v2

Mathematics

Algebraic Geometry

42 pages

Scientific paper

We study a conjectural relationship among Donaldson-Thomas type invariants on Calabi-Yau 3-folds counting torsion sheaves supported on ample divisors, ideal sheaves of curves and Pandharipande-Thomas's stable pairs. The conjecture is a mathematical formulation of Denef-Moore's formula derived in the study of Ooguri-Strominger-Vafa's conjecture relating black hole entropy and topological string. The main result of this paper is to prove our conjecture assuming a conjectural Bogomolov-Gieseker type inequality proposed by Bayer, Macri and the author.

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