Translator Disclaimer
15 July 2009 Limit stable objects on Calabi-Yau 3-folds
Yukinobu Toda
Author Affiliations +
Duke Math. J. 149(1): 157-208 (15 July 2009). DOI: 10.1215/00127094-2009-038

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

Citation

Download Citation

Yukinobu Toda. "Limit stable objects on Calabi-Yau 3-folds." Duke Math. J. 149 (1) 157 - 208, 15 July 2009. https://doi.org/10.1215/00127094-2009-038

Information

Published: 15 July 2009
First available in Project Euclid: 1 July 2009

zbMATH: 1172.14007
MathSciNet: MR2541209
Digital Object Identifier: 10.1215/00127094-2009-038

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

Rights: Copyright © 2009 Duke University Press

JOURNAL ARTICLE
52 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.149 • No. 1 • 15 July 2009
Back to Top