Jumping numbers of analytic multiplier ideals (with an appendix by Sébastien Boucksom)

Kim, Dano; Seo, Hoseob

doi:10.48550/arxiv.1908.02474

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Log Canonical Singularities Of Plurisubharmonic Functions1

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2020

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“…(cf. [33], Theorem 2.2) For each Siu plurisubharmonic function ϕ a • defined above on Ω ⊂ X, it follow that…”

Section: Log Canonical Singularities Of Plurisubharmonic Functionsmentioning

confidence: 98%

A note on multiplier ideal sheaves on complex spaces with singularities

2020

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The goal of this note is to present some recent results of our research concerning multiplier ideal sheaves on complex spaces and singularities of plurisubharmonic functions. We firstly introduce multiplier ideal sheaves on complex spaces (not necessarily normal) via Ohsawa's extension measure, as a special case of which, it turns out to be the so-called Mather-Jacobian multiplier ideals in the algebro-geometric setting. As applications, we obtain a reasonable generalization of (algebraic) adjoint ideal sheaves to the analytic setting and establish some extension theorems on Kähler manifolds from singular hypersurfaces. Relying on our multiplier and adjoint ideals, we also give characterizations for several important classes of singularities of pairs associated to plurisubharmonic functions.Moreover, we also investigate the local structure of singularities of log canonical locus of plurisubharmonic functions. Especially, in the three-dimensional case, we show that for any plurisubharmonic function with log canonical singularities, its associated multiplier ideal subscheme is weakly normal, by which we give a complete classification of multiplier ideal subschemes with log canonical singularities.

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“…(cf. [33], Theorem 2.2) For each Siu plurisubharmonic function ϕ a • defined above on Ω ⊂ X, it follow that…”

Section: Log Canonical Singularities Of Plurisubharmonic Functionsmentioning

confidence: 98%

A note on multiplier ideal sheaves on complex spaces with singularities

2020

Preprint

View full text Add to dashboard Cite

show abstract

Jumping numbers of analytic multiplier ideals (with an appendix by Sébastien Boucksom)

Cited by 1 publication

References 0 publications

A note on multiplier ideal sheaves on complex spaces with singularities

A note on multiplier ideal sheaves on complex spaces with singularities

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