Ohsawa-Takegoshi Extension Theorem for Compact Kähler Manifolds and Applications

Cao, Junyan

doi:10.1007/978-3-319-62914-8_2

Cited by 42 publications

(33 citation statements)

References 18 publications

(46 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The proof of the sharp estimate is due to B locki and Guan-Zhou [B lo13, GZ15]. There is also a (weaker) version of the Ohsawa-Takegoshi theorem for the case where the fibers are compact Kähler manifolds, proved by Cao [Cao14].…”

Section: Note a More Conceptual Description Involves The Fourier-mukmentioning

confidence: 99%

Algebraic fiber spaces over abelian varieties: Around a recent theorem by Cao and Păun

Hacon¹,

Popa²,

Schnell³

2018

Contemporary Mathematics

View full text Add to dashboard Cite

We present a simplified proof for a recent theorem by Junyan Cao and Mihai Pȃun, confirming a special case of Iitaka's Cn,m conjecture: if f : X → Y is an algebraic fiber space, and if the Albanese mapping of Y is generically finite over its image, then we have the inequality of Kodaira dimensions κ(X) ≥ κ(Y ) + κ(F ), where F denotes a general fiber of f . We include a detailed survey of the main algebraic and analytic techniques, especially the construction of singular hermitian metrics on pushforwards of adjoint bundles (due to Berndtsson, Pȃun, and Takayama).

show abstract

Section: Note a More Conceptual Description Involves The Fourier-mukmentioning

confidence: 99%

Algebraic fiber spaces over abelian varieties: Around a recent theorem by Cao and Păun

Hacon¹,

Popa²,

Schnell³

2018

Contemporary Mathematics

View full text Add to dashboard Cite

show abstract

“…We obtain J(h 1 a F ) = O X ′ since i E i + j F j has simple normal crossing supports and 0 < β j < 1. By [Cao,Theorem 3.5], there exists an a-th Bergman type metric h a,B on…”

Section: On a Log Casementioning

confidence: 99%

On the global generation of direct images of pluri-adjoint line bundles

Iwai

2019

Math. Z.

View full text Add to dashboard Cite

show abstract

“…The multiplier ideal sheaf I m (h) ⊂ O X is defined as follows. If ϕ is a local weight of h on some open set U ⊂ X, then the germ of I m (h) at a point p ∈ U consists of the germs of holomorphic functions f at p such that |f | 2/m e −ϕ/m is integrable at p. It is known that I(h 1/m ) is a coherent analytic sheaf on X [8].…”

Section: Introductionmentioning

confidence: 99%

Linear invariants of complex manifolds and their plurisubharmonic variations

Deng

Wang

Zhang

et al. 2020

Journal of Functional Analysis

View full text Add to dashboard Cite

For a bounded domain D and a real number p > 0, we denote by A p (D) the space of L p integrable holomorphic functions on D, equipped with the L p -pseudonorm. We prove that two bounded hyperconvex domains D 1 ⊂ C n and D 2 ⊂ C m are biholomorphic (in particular n = m) if there is a linear isometry between A p (D 1 ) and A p (D 2 ) for some 0 < p < 2. The same result holds for p > 2, p = 2, 4, · · · , provided that the p-Bergman kernels on D 1 and D 2 are exhaustive. With this as a motivation, we show that, for all p > 0, the p-Bergman kernel on a strongly pseudoconvex domain with C 2 boundary or a simply connected homogeneous regular domain is exhaustive. These results shows that spaces of pluricanonical sections of complex manifolds equipped with canonical pseudonorms are important invariants of complex manifolds. The second part of the present work devotes to studying variations of these invariants. We show that the direct image sheaf of the twisted relative mpluricanonical bundle associated to a holomorphic family of Stein manifolds or compact Kähler manifolds is positively curved, with respect to the canonical singular Finsler metric.2010 Mathematics Subject Classification. 53C55, 32Q57, 32Q15, 53C65.

show abstract

Ohsawa-Takegoshi Extension Theorem for Compact Kähler Manifolds and Applications

Abstract: Abstract. Our main goal in this article is to prove an extension theorem for sections of the canonical bundle of a weakly pseudoconvex Kähler manifold with values in a line bundle endowed with a possibly singular metric. We also give some applications of our result.

Cited by 42 publications

References 18 publications

Algebraic fiber spaces over abelian varieties: Around a recent theorem by Cao and Păun

Algebraic fiber spaces over abelian varieties: Around a recent theorem by Cao and Păun

On the global generation of direct images of pluri-adjoint line bundles

Linear invariants of complex manifolds and their plurisubharmonic variations

Contact Info

Product

Resources

About