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arXiv · 2512.19830

Singular Gauduchon Conjecture

Guilherme Cerqueira-Gonçalves
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Abstract

In 1984 Gauduchon conjectured that one can find Gauduchon metrics with prescribed Ricci curvature on all compact complex manifolds. This conjecture was settled by Sz\'ekelyhidi-Tosatti-Weinkove (TW17, TW19, STW17) by the study of the Monge-Amp\`ere equation for $(n-1)$-plurisubharmonic functions with a gradient term. In this paper we study a singular version of this conjecture. We obtain a $C^{0}$-estimate for this problem, without gradient terms, in smoothable hermitian variaties by adapting a recent technique of Guedj-Lu. We also prove the smoothness of solutions on holomorphic K\"ahler families, generalizing TW17.

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BibTeXRIS

Guilherme Cerqueira-Gonçalves. 2025-12-22. Singular Gauduchon Conjecture. https://arxiv.org/abs/2512.19830

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