Vol. 260, No. 2, 2012

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On occult period maps

Stephen Kudla and Michael Rapoport

Vol. 260 (2012), No. 2, 565–582
Abstract

We interpret the “occult” period maps of Allcock, Carlson, and Toledo (2002; 2011), of Looijenga and Swierstra (2007; 2008), and of Kondō (2000; 2002) in moduli theoretic terms, as a construction of certain families of polarized abelian varieties of Picard type. We show that these period maps are morphisms defined over their natural field of definition.

Keywords
Torelli theorems, period maps
Mathematical Subject Classification 2010
Primary: 11G15, 14D20, 14K22
Milestones
Received: 28 February 2012
Accepted: 27 September 2012
Published: 30 November 2012
Authors
Stephen Kudla
Department of Mathematics
University of Toronto
40 St. George St., BA6290
Toronto, ON  M5S 2E4
Canada
Michael Rapoport
Mathematisches Institut
Universität Bonn
Endenicher Allee 60
53115 Bonn
Germany