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

Xiaoli Han , Xishen Jin

Communications in Mathematics and Statistics ›› : 1 -9.

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Communications in Mathematics and Statistics ›› : 1 -9. DOI: 10.1007/s40304-025-00445-6
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Limit Behavior of Deformed Hermitian–Yang–Mills Metrics on Kähler Surfaces

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Abstract

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

Fm
on
Lm
where L is an ample line bundle over a Kähler surface
(X,ω)
. If the cohomology class
c1(L)
admits a solution of the J-equation, then we prove that
Fm
will converge to it. Furthermore, we also consider a boundary case. In this case, we prove that
Fm
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

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Xiaoli Han, Xishen Jin. Limit Behavior of Deformed Hermitian–Yang–Mills Metrics on Kähler Surfaces. Communications in Mathematics and Statistics 1-9 DOI:10.1007/s40304-025-00445-6

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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

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