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<p>In this paper, we prove that there exists a solution of the <i>J</i>-equation on the total space of a holomorphic submersion if there exist solutions of the <i>J</i>-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 <i>J</i>-nef, then each fiber is <i>J</i>-nef. In addition, if each fiber has a solution of the <i>J</i>-equation, then the base is also <i>J</i>-nef. Furthermore, we establish similar phenomena for the deformed Hermitian-Yang-Mills equation.</p>

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

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  • 发表日期：

    2026年2月28日

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  • Rei Murakami

摘要

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.