The deformed Hermitian-Yang-Mills equation on the blowup of ${\mathbb{P}}^n$

Abstract

We study the deformed Hermitian-Yang-Mills equation on the blowup of complex projective space. Using symmetry, we express the equation as an ODE which can be solved using combinatorial methods if an algebraic stability condition is satisfied. This gives evidence towards a conjecture of the first author, T.C. Collins, and S.-T. Yau on general compact Kahler manifolds.

arXiv commentThis version contains a slightly more general stability which is demonstrated to be sufficient for existence. It also corrects an error in the previous version which incorrectly stated stability was necessary. Instead, this version contains a new theorem demonstrating stability is necessary given an angle lifting assumption. 20 pages