Moduli of Bridgeland semistable objects on 3-folds and Donaldson-Thomas invariants
Algebraic Geometry
2016-01-28 v2
Abstract
We show that the moduli stacks of Bridgeland semistable objects on smooth projective 3-folds are proper algebraic stacks of finite type, if they satisfy the Bogomolov-Gieseker (BG for short) inequality conjecture proposed by Bayer, Macr\`i and the second author. The key ingredients are the equivalent form of the BG inequality conjecture and its generalization to arbitrary very weak stability conditions. This result is applied to define Donaldson-Thomas invariants counting Bridgeland semistable objects on smooth projective Calabi-Yau 3-folds satisfying the BG inequality conjecture, for example on \'etale quotients of abelian 3-folds.
Keywords
Cite
@article{arxiv.1504.01177,
title = {Moduli of Bridgeland semistable objects on 3-folds and Donaldson-Thomas invariants},
author = {Dulip Piyaratne and Yukinobu Toda},
journal= {arXiv preprint arXiv:1504.01177},
year = {2016}
}
Comments
Revised following referee comments, 44 pages, to appear in Crelle Journal