Bogomolov-Gieseker type inequality and counting invariants
Algebraic Geometry
2014-02-26 v3 High Energy Physics - Theory
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.
Keywords
Cite
@article{arxiv.1112.3411,
title = {Bogomolov-Gieseker type inequality and counting invariants},
author = {Yukinobu Toda},
journal= {arXiv preprint arXiv:1112.3411},
year = {2014}
}
Comments
42 pages, Lemma 3.16 is added, to appear in Journal of Topology