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Geometry and Physics: Volume IA Festschrift in honour of Nigel Hitchin$
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Andrew Dancer, Jørgen Ellegaard Andersen, and Oscar García-Prada

Print publication date: 2018

Print ISBN-13: 9780198802013

Published to Oxford Scholarship Online: December 2018

DOI: 10.1093/oso/9780198802013.001.0001

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The Deformed Hermitian–Yang–Mills Equation in Geometry and Physics

The Deformed Hermitian–Yang–Mills Equation in Geometry and Physics

(p.69) 4 The Deformed Hermitian–Yang–Mills Equation in Geometry and Physics
Geometry and Physics: Volume I

Tristan C. Collins

Dan Xie

Shing-Tung Yau

Oxford University Press

This chapter provides an introduction to the mathematics and physics of the deformed Hermitian–Yang–Mills equation, a fully non-linear geometric PDE on Kähler manifolds, which plays an important role in mirror symmetry. The chapter discusses the physical origin of the equation, and some recent progress towards its solution. In addition, in dimension 3, it proves a new Chern number inequality and discusses the relationship with algebraic stability conditions.

Keywords:   Hermitian–Yang–Mills, mirror symmetry, stability condition, Kähler manifold, Chern number

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