Duke Mathematical Journal

Limit stable objects on Calabi-Yau 3-folds

Yukinobu Toda

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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

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

First available in Project Euclid: 1 July 2009

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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


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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