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THE GEOMETRY AND ARITHMETIC OF A CALABI–YAU SIEGEL THREEFOLD

S. CYNK

Institute of Mathematics, Jagiellonian University, Łojasiewicza 6, 30–348 Kraków, Poland

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E. FREITAG

Mathematisches Institut, University of Heidelberg, Im Neuenheimer Feld 288, D69120 Heidelberg, Germany

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, and

R. SALVATI MANNI

Dipartimento di Matematica, Università La Sapienza, Piazzale Aldo, Moro 2, I 00185 Roma, Italy

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https://doi.org/10.1142/S0129167X1100732XCited by:1 (Source: Crossref)

Abstract

In this paper we treat in details a Siegel modular variety that has a Calabi–Yau model, . We shall describe the structure of the ring of modular forms and its geometry. We shall illustrate two different methods of producing the Hodge numbers. The first uses the definition of as the quotient of another known Calabi–Yau variety . In this case we will get the Hodge numbers considering the action of the group on a crepant resolution of . The second, purely algebraic geometric, uses the equations derived from the ring of modular forms and is based on determining explicitly the Calabi–Yau model and computing the Picard group and the Euler characteristic.

Keywords:

AMSC: Primary 11F46, Secondary 14J32

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