Strong (δ, n)-Complements for Semi-Stable Morphisms

Stefano Filipazzi; Joaqu´ın Moraga

doi:10.25537/dm.2020v25.1953-1996

Strong (δ, n)-Complements for Semi-Stable Morphisms

Stefano Filipazzi, Joaqu´ın Moraga

Mathematics

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

Abstract

We prove the boundedness of global strong (δ, n)- complements for generalized ∈-log canonical pairs of Fano-type. We also prove some partial results towards boundedness of local strong (δ, n)-complements for semi-stable morphisms. As applications, we prove an effective generalized canonical bundle formula for generalized klt pairs and an effective generalized adjunction formula for exceptional generalized log canonical centers. Moreover, we prove that the existence of strong (δ, n)-complements implies a conjecture due to McKernan concerning the singularities of the base of a Mori fiber space.

Original language	English (US)
Pages (from-to)	1953-1996
Number of pages	44
Journal	Documenta Mathematica
Volume	25
DOIs	https://doi.org/10.25537/dm.2020v25.1953-1996
State	Published - 2020

All Science Journal Classification (ASJC) codes

Mathematics(all)

Keywords

Complements
Fano-type varieties

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10.25537/dm.2020v25.1953-1996

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title = "Strong (δ, n)-Complements for Semi-Stable Morphisms",

abstract = "We prove the boundedness of global strong (δ, n)- complements for generalized ∈-log canonical pairs of Fano-type. We also prove some partial results towards boundedness of local strong (δ, n)-complements for semi-stable morphisms. As applications, we prove an effective generalized canonical bundle formula for generalized klt pairs and an effective generalized adjunction formula for exceptional generalized log canonical centers. Moreover, we prove that the existence of strong (δ, n)-complements implies a conjecture due to McKernan concerning the singularities of the base of a Mori fiber space.",

keywords = "Complements, Fano-type varieties",

author = "Stefano Filipazzi and Joaqu´ın Moraga",

note = "Funding Information: The authors would like to thank Christopher Hacon and Karl Schwede for many useful comments. They would also like to thank an anonymous referee for the careful report and several suggestions. The first named author was supported by the Graduate Research Fellowship awarded by the University of Utah. The two authors were partially supported by NSF research grants no: DMS-1801851, DMS-1265285 and by a grant from the Simons Foundation, Award Number: 256202. Publisher Copyright: {\textcopyright} 2020, Documenta Mathematica. All Rights Reserved.",

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T1 - Strong (δ, n)-Complements for Semi-Stable Morphisms

AU - Filipazzi, Stefano

AU - Moraga, Joaqu´ın

N1 - Funding Information: The authors would like to thank Christopher Hacon and Karl Schwede for many useful comments. They would also like to thank an anonymous referee for the careful report and several suggestions. The first named author was supported by the Graduate Research Fellowship awarded by the University of Utah. The two authors were partially supported by NSF research grants no: DMS-1801851, DMS-1265285 and by a grant from the Simons Foundation, Award Number: 256202. Publisher Copyright: © 2020, Documenta Mathematica. All Rights Reserved.

PY - 2020

Y1 - 2020

N2 - We prove the boundedness of global strong (δ, n)- complements for generalized ∈-log canonical pairs of Fano-type. We also prove some partial results towards boundedness of local strong (δ, n)-complements for semi-stable morphisms. As applications, we prove an effective generalized canonical bundle formula for generalized klt pairs and an effective generalized adjunction formula for exceptional generalized log canonical centers. Moreover, we prove that the existence of strong (δ, n)-complements implies a conjecture due to McKernan concerning the singularities of the base of a Mori fiber space.

AB - We prove the boundedness of global strong (δ, n)- complements for generalized ∈-log canonical pairs of Fano-type. We also prove some partial results towards boundedness of local strong (δ, n)-complements for semi-stable morphisms. As applications, we prove an effective generalized canonical bundle formula for generalized klt pairs and an effective generalized adjunction formula for exceptional generalized log canonical centers. Moreover, we prove that the existence of strong (δ, n)-complements implies a conjecture due to McKernan concerning the singularities of the base of a Mori fiber space.

KW - Complements

KW - Fano-type varieties

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SP - 1953

EP - 1996

JO - Documenta Mathematica

JF - Documenta Mathematica

ER -

Strong (δ, n)-Complements for Semi-Stable Morphisms

Abstract

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