Open Access
VOL. 59 | 2010 Generating functions of stable pair invariants via wall-crossings in derived categories
Chapter Author(s) Yukinobu Toda
Editor(s) Masa-Hiko Saito, Shinobu Hosono, Kōta Yoshioka
Adv. Stud. Pure Math., 2010: 389-434 (2010) DOI: 10.2969/aspm/05910389

Abstract

The notion of limit stability on Calabi–Yau 3-folds is introduced by the author to construct an approximation of Bridgeland–Douglas stability conditions at the large volume limit. It has also turned out that the wall-crossing phenomena of limit stable objects seem relevant to the rationality conjecture of the generating functions of Pandharipande–Thomas invariants. In this article, we shall make it clear how wallcrossing formula of the counting invariants of limit stable objects solves the above conjecture.

Information

Published: 1 January 2010
First available in Project Euclid: 24 November 2018

zbMATH: 1216.14009
MathSciNet: MR2683216

Digital Object Identifier: 10.2969/aspm/05910389

Subjects:
Primary: 14D20
Secondary: 14J32 , 18E30

Keywords: Donaldson–Thomas invariant , stability condition

Rights: Copyright © 2010 Mathematical Society of Japan

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