Bounding singular surfaces via Chern numbers

Joaquín Moraga

doi:10.1007/s00209-019-02409-3

Bounding singular surfaces via Chern numbers

Joaquín Moraga

Mathematics

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

Abstract

We prove the existence of a bound on the number of steps of the minimal model program for singular surfaces in terms of discrepancies and Chern numbers. As an application, we prove that given R∈ R_{> 0} and ϵ∈ (0 , 1) , the class F(R, ϵ) of 2-dimensional pairs (X, D) of general type with ϵ-klt singularities, D with standard coefficients, and 4c2(X,D)-c12(X,D)≤R, forms a bounded family.

Original language	English (US)
Pages (from-to)	1597-1614
Number of pages	18
Journal	Mathematische Zeitschrift
Volume	295
Issue number	3-4
DOIs	https://doi.org/10.1007/s00209-019-02409-3
State	Published - Aug 1 2020

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1007/s00209-019-02409-3

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abstract = "We prove the existence of a bound on the number of steps of the minimal model program for singular surfaces in terms of discrepancies and Chern numbers. As an application, we prove that given R∈ R> 0 and ϵ∈ (0 , 1) , the class F(R, ϵ) of 2-dimensional pairs (X, D) of general type with ϵ-klt singularities, D with standard coefficients, and 4c2(X,D)-c12(X,D)≤R, forms a bounded family.",

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AB - We prove the existence of a bound on the number of steps of the minimal model program for singular surfaces in terms of discrepancies and Chern numbers. As an application, we prove that given R∈ R> 0 and ϵ∈ (0 , 1) , the class F(R, ϵ) of 2-dimensional pairs (X, D) of general type with ϵ-klt singularities, D with standard coefficients, and 4c2(X,D)-c12(X,D)≤R, forms a bounded family.

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U2 - 10.1007/s00209-019-02409-3

DO - 10.1007/s00209-019-02409-3

M3 - Article

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EP - 1614

JO - Mathematische Zeitschrift

JF - Mathematische Zeitschrift

IS - 3-4

ER -

Bounding singular surfaces via Chern numbers

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