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Limit stable objects on Calabi-Yau 3-folds
Yukinobu Toda
Source: Duke Math. J. Volume 149, Number 1 (2009), 157-208.
Abstract
In this article, we introduce new enumerative invariants of curves on Calabi-Yau $3$-folds via certain stable objects in the derived category of coherent sheaves. We introduce the notion of limit stability on the category of perverse coherent sheaves, a subcategory in the derived category, and construct the moduli spaces of limit stable objects. We then define the counting invariants of limit stable objects using Behrend's constructible functions on those moduli spaces. It will turn out that our invariants are generalizations of counting invariants of stable pairs introduced by Pandharipande and Thomas. We will also investigate the wall-crossing phenomena of our invariants under change of stability conditions
Primary Subjects: 14D20
Secondary Subjects: 14J32, 18E30
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.dmj/1246453791
Digital Object Identifier: doi:10.1215/00127094-2009-038
Zentralblatt MATH identifier:
05588174
Mathematical Reviews number (MathSciNet):
MR2541209
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