Duke Mathematical Journal

Limit stable objects on Calabi-Yau 3-folds

Yukinobu Toda

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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

Article information

Source
Duke Math. J., Volume 149, Number 1 (2009), 157-208.

Dates
First available in Project Euclid: 1 July 2009

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1246453791

Digital Object Identifier
doi:10.1215/00127094-2009-038

Mathematical Reviews number (MathSciNet)
MR2541209

Zentralblatt MATH identifier
1172.14007

Subjects
Primary: 14D20: Algebraic moduli problems, moduli of vector bundles {For analytic moduli problems, see 32G13}
Secondary: 14J32: Calabi-Yau manifolds 18E30: Derived categories, triangulated categories

Citation

Toda, Yukinobu. Limit stable objects on Calabi-Yau 3-folds. Duke Math. J. 149 (2009), no. 1, 157--208. doi:10.1215/00127094-2009-038. https://projecteuclid.org/euclid.dmj/1246453791


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