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arXiv · 1112.3411

Bogomolov-Gieseker type inequality and counting invariants

Yukinobu Toda
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Abstract

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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Yukinobu Toda. 2012-10-16. Bogomolov-Gieseker type inequality and counting invariants. https://doi.org/10.1112/jtopol%2Fjts037

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