Endomorphism rings of abelian surfaces and projective models of their moduli spaces

Authors
Citation
B. Runge, Endomorphism rings of abelian surfaces and projective models of their moduli spaces, TOHOKU MATH, 51(3), 1999, pp. 283-303
Citations number
29
Language
INGLESE
art.tipo
Article
Categorie Soggetti
Mathematics
Journal title
TOHOKU MATHEMATICAL JOURNAL
ISSN journal
0040-8735 → ACNP
Volume
51
Issue
3
Year of publication
1999
Pages
283 - 303
Database
ISI
SICI code
0040-8735(199909)51:3<283:EROASA>2.0.ZU;2-3
Abstract
We construct projective models for Humbert surfaces and QCM-curves, i.e., S himura curves together with their natural embedding into the coarse moduli space for principally polarized abelian surfaces. The points of a QCM-curve correspond to an abelian surface, such that its algebra of complex multipl ications is an order in an indefinite rational quaternian algebra. Moreover , we determine the structure of such orders.