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Bounding singular surfaces via Chern numbers

  • Joaquín MoragaEmail author
Article

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 \(R\in {\mathbb {R}}_{>0}\) and \(\epsilon \in (0,1)\), the class \({\mathcal {F}}(R,\epsilon )\) of 2-dimensional pairs (XD) of general type with \(\epsilon \)-klt singularities, D with standard coefficients, and \(4c_2(X,D)-c_1^2(X,D)\le R\), forms a bounded family.

Mathematics Subject Classification

Primary 14E30 Secondary 14J17 

Notes

Acknowledgements

The author would like to thank Christopher Hacon and Valery Alexeev for many useful comments. He would like to express his gratitude to the anonymous referees for their careful report and the many suggestions.

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© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of MathematicsPrinceton UniversityPrincetonUSA

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