Asian Journal of Mathematics

Volume 26 (2022)

Number 6

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

Pages: 847 – 864

DOI: https://dx.doi.org/10.4310/AJM.2022.v26.n6.a4

Authors

Adam Jacob (Department of Mathematics, University of California, Davis, Calif., U.S.A.)

Norman Sheu (Department of Mathematics, University of California, Berkeley, Calif., U.S.A.)

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 Kähler manifolds.

Keywords

deformed Hermitian–Yang–Mills, stability, Calabi symmetry, ODEs

2010 Mathematics Subject Classification

53C55

Full Text (PDF format)

The first-named author was supported in part by a Simons Collaboration Grant.

Received 16 January 2022

Accepted 15 September 2022

Published 27 April 2023