Compositio Mathematica

Calabi–Yau Threefolds and Moduli of Abelian Surfaces I

Mark Gross a1 and Sorin Popescu a2
a1 Mathematics Institute, University of Warwick, Coventry CV4 7AL, U.K. E-mail:
a2 Department of Mathematics, Columbia University, New York, NY 10027, U.S.A. E-mail:

Article author query
gross m   [Google Scholar] 
popescu s   [Google Scholar] 


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.

Key Words: Abelian surfaces; moduli; rationality; Calabi–Yau threefolds.