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Desingularized fiber products of semi-stable elliptic surfaces with vanishing third Betti number

Part of: Arithmetic problems. Diophantine geometry Families, fibrations Surfaces and higher-dimensional varieties

Published online by Cambridge University Press:  01 January 2009

Chad Schoen
Chad Schoen*
Affiliation:
Department of Mathematics, Duke University, Box 90320, Durham, NC 27708-0320, USA (email: [email protected])
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Abstract

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Desingularized fiber products of semi-stable elliptic surfaces with Hetale3=0 are classified. Such varieties may play a role in the study of supersingular threefolds, of the deformation theory of varieties with trivial canonical bundle, and of arithmetic degenerations of rigid Calabi–Yau threefolds.

Keywords

supersingular threefoldCalabi–Yau threefoldfiber product of elliptic surfaces

MSC classification

Secondary: 14D06: Fibrations, degenerations 14J32: Calabi-Yau manifolds 14G15: Finite ground fields
Type
Research Article
Information
Compositio Mathematica , Volume 145 , Issue 1 , January 2009 , pp. 89 - 111
Copyright
Copyright © Foundation Compositio Mathematica 2009

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