Quantitative extensions of pluricanonical forms and closed positive currents

Берндтссон, Бо; Păun, Mihai

doi:10.1215/00277630-1543778

Cited by 25 publications

(28 citation statements)

References 40 publications

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“…The authors also show the injectivity of p by a ingenious use of Khovanskii-Teissier inequalities 3. In particular, if the algebraic fundamental group π 1 (X) of X is trivial 4.…”

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confidence: 92%

Foliations with positive slopes and birational stability of orbifold cotangent bundles

Campana

Păun

2019

Publ.math.IHES

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Let X be a smooth connected projective manifold, together with an snc orbifold divisor ∆, such that the pair (X, ∆) is log-canonical. If K X + ∆ is not pseudo-effective, we show, among other things, that any quotient of its orbifold cotangent bundle has a pseudo-effective determinant. This improves considerably our previous result [18], where generic positivity instead of pseudoeffectivity was obtained. One of the new ingredients in the proof is a version of the Bogomolov-McQuillan algebraicity criterion for holomorphic foliations whose minimal slope with respect to a movable class (instead of an ample complete intersection class) is positive.

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“…The authors also show the injectivity of p by a ingenious use of Khovanskii-Teissier inequalities 3. In particular, if the algebraic fundamental group π 1 (X) of X is trivial 4.…”

mentioning

confidence: 92%

Foliations with positive slopes and birational stability of orbifold cotangent bundles

Campana

Păun

2019

Publ.math.IHES

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“…Let us first recall the strategy of the proof in the case where D = 0 ([Pȃu12, Theorem 1.1]). First, one proves that the current ρ is positive on X 0 , and then one proves that it extends to a positive current on X using a refined version of Ohsawa Takegoshi theorem [BP12].…”

Section: Introductionmentioning

confidence: 99%

Families of conic Kähler–Einstein metrics

Guenancia

2018

Math. Ann.

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Let p : X → Y be an holomorphic surjective map between compact Kähler manifolds and let D be an effective divisor on X with generically simple normal crossings support and coefficients in (0, 1). Provided that the adjoint canonical bundle KX y + Dy of the generic fiber is ample, we show that the current obtained by glueing the fiberwise conic Kähler-Einstein metrics on the regular locus of the fibration is positive. Moreover, we prove that this current is bounded outside the divisor and that it extends to a positive current on X.

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“…Berndtsson, Pȃun[1]). There exists a holomorphic functionf on U and positive constant C 0 independent of m and y satisfyingf | Uy = f on U y andU |f | 2/m dV z ≤ C 0 Uy |f | 2/m dV z p * dV s .Choose U ⊂⊂ U so that the geodesic ball B ǫ (x) of radius ǫ satisfying B ǫ (x) ⊂ U for all x ∈ V .…”

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confidence: 99%

Holomorphic Families of Strongly Pseudoconvex Domains in a Kähler Manifold

Choi

Yoo

2020

J Geom Anal

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Let p : X → Y be a surjective holomorphic mapping between Kähler manifolds. Let D be a bounded smooth domain in X such that every generic fiber D y := D ∩ p −1 (y) for y ∈ Y is a strongly pseudoconvex domain in X y := p −1 (y), which admits the complete Kähler-Einstein metric. This family of Kähler-Einstein metrics induces a smooth (1, 1)-form ρ on D. In this paper, we prove that ρ is positive-definite on D if D is strongly pseudoconvex. We also discuss the extensioin of ρ as a positive current across singular fibers.

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Quantitative extensions of pluricanonical forms and closed positive currents

Abstract: Abstract. We establish here several "invariance of plurigenera type" theorems for twisted pluricanonical forms and metrics of adjoint R-bundles.

Cited by 25 publications

References 40 publications

Foliations with positive slopes and birational stability of orbifold cotangent bundles

Foliations with positive slopes and birational stability of orbifold cotangent bundles

Families of conic Kähler–Einstein metrics

Holomorphic Families of Strongly Pseudoconvex Domains in a Kähler Manifold

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