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Journal für die reine und angewandte Mathematik

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Volume 2019, Issue 747

Issues

Moduli of Bridgeland semistable objects on 3-folds and Donaldson–Thomas invariants

Dulip Piyaratne
  • Kavli Institute for the Physics and Mathematics of the Universe, University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa, 277-8583, Japan
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/ Yukinobu Toda
  • Kavli Institute for the Physics and Mathematics of the Universe, University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa, 277-8583, Japan
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Published Online: 2016-06-19 | DOI: https://doi.org/10.1515/crelle-2016-0006

Abstract

In this paper we show that the moduli stacks of Bridgeland semistable objects on smooth projective 3-folds are quasi-proper algebraic stacks of finite type if they satisfy the Bogomolov–Gieseker (BG for short) inequality conjecture proposed by Bayer, Macrì 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 étale quotients of abelian 3-folds.

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About the article

Received: 2015-04-13

Revised: 2016-01-09

Published Online: 2016-06-19

Published in Print: 2019-02-01


Funding Source: Ministry of Education, Culture, Sports, Science, and Technology

Award identifier / Grant number: 26287002

This work is supported by World Premier International Research Center Initiative (WPI initiative), MEXT, Japan. The second author is also supported by Grant-in Aid for Scientific Research grant (No. 26287002) from the Ministry of Education, Culture, Sports, Science and Technology, Japan.


Citation Information: Journal für die reine und angewandte Mathematik (Crelles Journal), Volume 2019, Issue 747, Pages 175–219, ISSN (Online) 1435-5345, ISSN (Print) 0075-4102, DOI: https://doi.org/10.1515/crelle-2016-0006.

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