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Smoothable del Pezzo surfaces with quotient singularities

Part of: Birational geometry Surfaces and higher-dimensional varieties

Published online by Cambridge University Press:  15 December 2009

Paul Hacking  and
Yuri Prokhorov
Paul Hacking
Affiliation:
Department of Mathematics and Statistics, Lederle Graduate Research Tower, Box 34515, University of Massachusetts Amherst, Amherst, MA 01003, USA (email: hacking@math.umass.edu)
Yuri Prokhorov
Affiliation:
Department of Higher Algebra, Faculty of Mathematics and Mechanics, Moscow State Lomonosov University, Vorobievy Gory, Moscow 119 899, Russia (email: prokhoro@mech.math.msu.su)
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Abstract

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We classify del Pezzo surfaces with quotient singularities and Picard rank one which admit a ℚ-Gorenstein smoothing. These surfaces arise as singular fibres of del Pezzo fibrations in the 3-fold minimal model program and also in moduli problems.

Keywords

del Pezzo surfacemoduliMori fiber space

MSC classification

Secondary: 14J10: Families, moduli, classification 14E30: Minimal model program (Mori theory, extremal rays)
Type
Research Article
Information
Compositio Mathematica , Volume 146 , Issue 1 , January 2010 , pp. 169 - 192
Copyright
Copyright © Foundation Compositio Mathematica 2009

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