Limit Behavior of Deformed Hermitian–Yang–Mills Metrics on Kähler Surfaces

Abstract

In this paper, we consider the limit behavior of a sequence of deformed Hermitian–Yang–Mills metrics

F_m

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on

L^{\otimes m}

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where L is an ample line bundle over a Kähler surface

(X,\omega )

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. If the cohomology class

c_1(L)

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admits a solution of the J-equation, then we prove that

F_m

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will converge to it. Furthermore, we also consider a boundary case. In this case, we prove that

F_m

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will converge to a singular Kähler metric away from a finite number of curves with negative self-intersection on the surface.

Keywords

Deformed Hermitian–Yang–Mills metric / J-equation / Monge–Ampére equation / Kähler surface

Funding

National Key R&D Program of China(2022YFA1005400)

NFSC(12031017)

RIGHTS & PERMISSIONS

School of Mathematical Sciences, University of Science and Technology of China and Springer-Verlag GmbH Germany, part of Springer Nature