Jumping numbers of analytic multiplier ideals (with an appendix by S

Kim, Dano; Seo, Hoseob

doi:10.4064/ap190529-19-12

Cited by 23 publications

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“…For example, if ϕ − ψ happens to be psh with vanishing Lelong numbers, then ϕ and ψ are v-equivalent. However that is a very special case: there are lots of examples of v-equivalent ϕ and ψ without ϕ − ψ being psh: see [KS19,(2.3), (2.9)].…”

Section: 3mentioning

confidence: 99%

Canonical bundle formula and degenerating families of volume forms

Kim

2019

Preprint

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For a degenerating family of projective manifolds, it is of fundamental interest to study the asymptotic behavior of integrals near singular fibers. In our main results, we determine the volume asymptotics (equivalently the asymptotics of L 2 metrics) in all base dimensions, which generalizes numerous previous results in base dimension 1.In the case of log Calabi-Yau fibrations, we establish a metric version of the canonical bundle formula (due to Kawamata and others): the L 2 metric carries the singularity equal to the discriminant divisor and the moduli part line bundle has a singular hermitian metric with vanishing Lelong numbers. This solves a problem which is implicit in Kawamata's work and recently raised again by Eriksson, Freixas i Montplet and Mourougane.As consequences, we strengthen the semipositivity theorems due to Fujita, Kawamata and others for log Calabi-Yau fibrations, giving an entirely new simpler proof which does not use Hodge theory, i.e. difficult results (e.g. Cattani-Kaplan-Schmid) in the theory of variation of Hodge structure. Instead, in the proof of our main results, together with the study of plurisubharmonic singularities, we use Berndtsson type results on the positivity of direct images. The fact that this much simpler and direct method can replace the use of Hodge theory in the proof of the semipositivity theorems answers a question of Berndtsson.

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Section: 3mentioning

confidence: 99%

Canonical bundle formula and degenerating families of volume forms

Kim

2019

Preprint

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“…I(ψ) = I + (ψ) := ∪ ǫ>0 I((1 + ǫ)ψ)) is an important feature of multiplier ideal sheaves and "opened the door to new types of approximation techniques" (see [38]) (see e.g. [27,35,4,5,15,6,46,30,3,47,48,16,36,7]). The strong openness property was conjectured by Demailly [10], and proved by Guan-Zhou [27] (the 2-dimensional case was proved by Jonsson-Mustat ¸ȃ [33]).…”

Section: Introductionmentioning

confidence: 99%

Boundary points, Minimal $L^{2}$ integrals and Concavity property

Bao¹,

Guan²,

Zheng³

2022

Preprint

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In this article, we consider minimal L 2 integrals on sublevel sets of a plurisubharmonic function with respect to a module at a boundary point of the sublevel sets, and establish a concavity property of the minimal L 2 integrals. As applications, we obtain a sharp effectiveness result related to a conjecture posed by Jonsson-Mustat ¸ȃ, which completes the approach from the conjecture to the strong openness property; we also obtain a strong openness property of the module and a lower semi-continuity property with respect to the module.

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“…I(ψ) = I + (ψ) := ∪ ǫ>0 I((1 + ǫ)ψ)) is an important feature and has been widely used in the study of several complex variables, complex algebraic geometry and complex differential geometry (see e.g. [38,46,8,9,21,10,58,41,6,59,60,22,47,11]), where ψ is a plurisubharmonic function on a complex manifold M (see [12]) and multiplier ideal sheaf I(ψ) is the sheaf of germs of holomorphic functions f such that |f | 2 e −ψ is locally integrable (see e.g. [56,49,51,15,16,14,17,48,52,53,13,42]).…”

Section: Introductionmentioning

confidence: 99%

Modules at boundary points, fiberwise Bergman kernels, and log-subharmonicity

Bao¹,

Guan²

2022

Preprint

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In this article, we consider Bergman kernels with respect to modules at boundary points, and obtain a log-subharmonicity property of the Bergman kernels, which deduces a concavity property related to the Bergman kernels. As applications, we reprove the sharp effectiveness result related to a conjecture posed by Jonsson-Mustatȃ and the effectiveness result of strong openness property of the modules at boundary points.

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Jumping numbers of analytic multiplier ideals (with an appendix by S

Cited by 23 publications

References 0 publications

Canonical bundle formula and degenerating families of volume forms

Canonical bundle formula and degenerating families of volume forms

Boundary points, Minimal $L^{2}$ integrals and Concavity property

Modules at boundary points, fiberwise Bergman kernels, and log-subharmonicity

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