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Moduli of surfaces with an anti-canonical cycle

Part of: Surfaces and higher-dimensional varieties

Published online by Cambridge University Press:  09 October 2014

Mark Gross ,
Paul Hacking  and
Sean Keel
Mark Gross
Affiliation:
DPMMS, Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WB, UK email mgross@dpmms.cam.ac.uk
Paul Hacking
Affiliation:
Department of Mathematics and Statistics, Lederle Graduate Research Tower, University of Massachusetts, Amherst, MA 01003-9305, USA email hacking@math.umass.edu
Sean Keel
Affiliation:
Department of Mathematics, 1 University Station C1200, Austin, TX 78712-0257, USA email keel@math.utexas.edu
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Abstract

We prove a global Torelli theorem for pairs $(Y,D)$ where $Y$ is a smooth projective rational surface and $D\in |-K_{Y}|$ is a cycle of rational curves, as conjectured by Friedman in 1984. In addition, we construct natural universal families for such pairs.

Keywords

Looijenga pairsrational surfacesmoduli

MSC classification

Primary: 14J26: Rational and ruled surfaces 14J10: Families, moduli, classification
Type
Research Article
Information
Compositio Mathematica , Volume 151 , Issue 2 , February 2015 , pp. 265 - 291
Copyright
© The Author(s) 2014 

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