Bounded deformations of (ε, δ) -log canonical singularities

Jingjun Han; Jihao Liu; Joaquin Moraga

Bounded deformations of (ε, δ) -log canonical singularities

Jingjun Han, Jihao Liu, Joaquin Moraga

Mathematics

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

5 Scopus citations

Abstract

In this paper we study (ε,δ)-lc singularites, i.e. ε-lc singularities admitting a δ-plt blow-up. We prove that n-dimensional (ε,δ)-lc singularities are bounded up to a deformation, and 2-dimensional (ε,δ)-lc singularities form a bounded family. Furthermore, we give an example which shows that (ε,δ)-lc singularities are not bounded in higher dimensions, even in the analytic sense.

Original language	English (US)
Pages (from-to)	1-28
Number of pages	28
Journal	Journal of Mathematical Sciences (Japan)
Volume	27
Issue number	1
State	Published - 2020

All Science Journal Classification (ASJC) codes

General Mathematics

Keywords

Bounded families
Deformations
Klt singularities
Log discrepancies
Plt blow-up

Cite this

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title = "Bounded deformations of (ε, δ) -log canonical singularities",

abstract = "In this paper we study (ε,δ)-lc singularites, i.e. ε-lc singularities admitting a δ-plt blow-up. We prove that n-dimensional (ε,δ)-lc singularities are bounded up to a deformation, and 2-dimensional (ε,δ)-lc singularities form a bounded family. Furthermore, we give an example which shows that (ε,δ)-lc singularities are not bounded in higher dimensions, even in the analytic sense.",

keywords = "Bounded families, Deformations, Klt singularities, Log discrepancies, Plt blow-up",

author = "Jingjun Han and Jihao Liu and Joaquin Moraga",

year = "2020",

language = "English (US)",

volume = "27",

pages = "1--28",

journal = "Journal of Mathematical Sciences (Japan)",

issn = "1340-5705",

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TY - JOUR

T1 - Bounded deformations of (ε, δ) -log canonical singularities

AU - Han, Jingjun

AU - Liu, Jihao

AU - Moraga, Joaquin

PY - 2020

Y1 - 2020

N2 - In this paper we study (ε,δ)-lc singularites, i.e. ε-lc singularities admitting a δ-plt blow-up. We prove that n-dimensional (ε,δ)-lc singularities are bounded up to a deformation, and 2-dimensional (ε,δ)-lc singularities form a bounded family. Furthermore, we give an example which shows that (ε,δ)-lc singularities are not bounded in higher dimensions, even in the analytic sense.

AB - In this paper we study (ε,δ)-lc singularites, i.e. ε-lc singularities admitting a δ-plt blow-up. We prove that n-dimensional (ε,δ)-lc singularities are bounded up to a deformation, and 2-dimensional (ε,δ)-lc singularities form a bounded family. Furthermore, we give an example which shows that (ε,δ)-lc singularities are not bounded in higher dimensions, even in the analytic sense.

KW - Bounded families

KW - Deformations

KW - Klt singularities

KW - Log discrepancies

KW - Plt blow-up

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M3 - Article

AN - SCOPUS:85103434094

SN - 1340-5705

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SP - 1

EP - 28

JO - Journal of Mathematical Sciences (Japan)

JF - Journal of Mathematical Sciences (Japan)

IS - 1

ER -

Bounded deformations of (ε, δ) -log canonical singularities

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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