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VOL. 65 | 2015 ADHM sheaf theory and wallcrossing
Wu-yen Chuang

Editor(s) Jungkai Alfred Chen, Meng Chen, Yujiro Kawamata, JongHae Keum

Abstract

In this article we survey the recent developments in ADHM sheaf theory on a smooth projective variety $X$. When $X$ is a curve the theory is an alternative construction of stable pair theory of Pandharipande and Thomas or Gromov–Witten theory on local curve geometries. The construction relies on relative Beilinson spectral sequence and Fourier–Mukai transformation. We will present some applications of the theory, including the derivations of the wallcrossing formulas, higher rank Donaldson–Thomas invariants on local curves, and the coholomogies of the moduli of stable Hitchin pairs.

Information

Published: 1 January 2015
First available in Project Euclid: 19 October 2018

zbMATH: 1360.14129
MathSciNet: MR3380776

Digital Object Identifier: 10.2969/aspm/06510083

Subjects:
Primary: 14N35
Secondary: 81T30

Rights: Copyright © 2015 Mathematical Society of Japan

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