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arXiv · 2208.08576

$J$-equations and deformed Hermitian-Yang-Mills equations on holomorphic submersions

Rei Murakami
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Abstract

In this paper, we prove that there exists a solution of the $J$-equation on the total space of a holomorphic submersion if there exist solutions of the $J$-equation on the fibers and the base. The method is an adiabatic limit technique. We also partially prove the converse implication. More precisely, if the total space is $J$-nef, then each fiber is $J$-nef. In addition, if each fiber has a solution of the $J$-equation, then the base is also $J$-nef. Furthermore, we establish similar phenomena for the deformed Hermitian-Yang-Mills equation.

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Rei Murakami. 2022-08-18. $J$-equations and deformed Hermitian-Yang-Mills equations on holomorphic submersions. https://arxiv.org/abs/2208.08576

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