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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
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
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