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arXiv · 2312.16140

Log canonical singularities of plurisubharmonic functions

Dano Kim·János Kollár
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Abstract

A plurisubharmonic weight is log canonical if it is at the critical point of turning non-integrable. Given a log canonical plurisubharmonic weight, we show that locally there always exists a log canonical `holomorphic' weight having the same non-integrable locus. The proof uses the theory of quasimonomial valuations developed by Jonsson-Musta\c{t}\v{a} and Xu, as well as the minimal model program over complex analytic spaces due to Fujino and Lyu-Murayama. As a consequence, we obtain that the non-integrable locus is seminormal.

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Dano Kim, János Kollár. 2023-12-26. Log canonical singularities of plurisubharmonic functions. https://arxiv.org/abs/2312.16140

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