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Calabi–Yau Threefolds and Moduli of Abelian Surfaces I

Published online by Cambridge University Press:  04 December 2007

Mark Gross  and
Sorin Popescu
Mark Gross
Affiliation:
Mathematics Institute, University of Warwick, Coventry CV4 7AL, U.K. E-mail: [email protected]
Sorin Popescu
Affiliation:
Department of Mathematics, Columbia University, New York, NY 10027, U.S.A. E-mail: [email protected]
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Abstract

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We describe birational models and decide the rationality/unirationality of moduli spaces $\cal A$d (and $\cal A$levd) of (1, d)-polarized Abelian surfaces (with canonical level structure, respectively) for small values of d. The projective lines identified in the rational/unirational moduli spaces correspond to pencils of Abelian surfaces traced on nodal threefolds living naturally in the corresponding ambient projective spaces, and whose small resolutions are new Calabi–Yau threefolds with Euler characteristic zero.

Keywords

Abelian surfacesmodulirationalityCalabi–Yau threefolds
Type
Research Article
Information
Compositio Mathematica , Volume 127 , Issue 2 , June 2001 , pp. 169 - 228
Copyright
© 2001 Kluwer Academic Publishers