The deformed Hermitian-Yang-Mills equation in geometry and physics
Tristan C. Collins, Dan Xie, Shing-Tung Yau
TL;DR
This paper introduces the deformed Hermitian-Yang-Mills equation, a nonlinear PDE on Kahler manifolds relevant to mirror symmetry, discussing its physical origins, recent progress, and new mathematical inequalities.
Contribution
It provides an overview of the equation's role in geometry and physics, proves a new Chern number inequality in dimension 3, and explores connections with algebraic stability.
Findings
Proved a new Chern number inequality in dimension 3
Discussed the physical origin and mathematical properties of the equation
Explored the relationship with algebraic stability conditions
Abstract
We provide an introduction to the mathematics and physics of the deformed Hermitian-Yang-Mills equation, a fully nonlinear geometric PDE on Kahler manifolds which plays an important role in mirror symmetry. We discuss the physical origin of the equation, and some recent progress towards its solution. In dimension 3 we prove a new Chern number inequality and discuss the relationship with algebraic stability conditions.
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Taxonomy
TopicsGeometry and complex manifolds · Nonlinear Waves and Solitons · Advanced Algebra and Geometry