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arxiv: 1112.3411 · v3 · pith:7Y7NOPJYnew · submitted 2011-12-15 · 🧮 math.AG · hep-th

Bogomolov-Gieseker type inequality and counting invariants

Yukinobu Toda This is my paper
classification 🧮 math.AG hep-th
keywords conjecturetypebogomolov-giesekerconjecturalcountinginequalityinvariantssheaves
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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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