2019
DOI: 10.48550/arxiv.1910.06917
|View full text |Cite
Preprint
|
Sign up to set email alerts
|

Canonical bundle formula and degenerating families of volume forms

Dano Kim

Abstract: 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 eq… Show more

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
1
1
1
1

Citation Types

1
9
0

Year Published

2019
2019
2021
2021

Publication Types

Select...
3

Relationship

1
2

Authors

Journals

citations
Cited by 3 publications
(10 citation statements)
references
References 40 publications
1
9
0
Order By: Relevance
“…1.3] 11 taking g : E → Y ′ in the place of X → Y in that statement. (Note that the fiber integral of [K19,Cor. 1.3] corresponds precisely to the direct image of a measure, cf.…”
Section: Proofs Of the Main Resultsmentioning
confidence: 99%
See 1 more Smart Citation
“…1.3] 11 taking g : E → Y ′ in the place of X → Y in that statement. (Note that the fiber integral of [K19,Cor. 1.3] corresponds precisely to the direct image of a measure, cf.…”
Section: Proofs Of the Main Resultsmentioning
confidence: 99%
“…There is a typo of 2a i in (4),[K19, Cor. 1.3] in the current version which should be corrected to −2a i .…”
mentioning
confidence: 99%
“…, and the asymptotic behavior of the volume form π * ω n can was obtained in [28, Theorems 2.3 and 7.1] using Hodge theory (and in [40] with a different method, which also extends to the case when the morphism f is Kähler but not projective, see [40,Rmk 1.6]): on Ñ \E we have…”
Section: Andmentioning
confidence: 95%
“…The canonical bundle formula. The exponents β j , γ i in (3.1) can be determined by applying the canonical bundle formula in birational geometry [1,21,24,39,40,42,21] to the map f . Following the notation in [40], we define divisors R = − D on M and M = −K Ñ on Ñ , so that we have the equality as Q-divisors…”
Section: 2mentioning
confidence: 99%
See 1 more Smart Citation