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Plurigenera of general type surfaces in mixed characteristic

Part of: Arithmetic problems. Diophantine geometry Surfaces and higher-dimensional varieties Algebraic groups

Published online by Cambridge University Press:  01 September 2008

Junecue Suh
Junecue Suh*
Affiliation:
Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA (email: junecuesuh@math.mit.edu)
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Abstract

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We construct general type surfaces in mixed characteristic whose geometric genera can be made to jump by an arbitrarily prescribed positive amount under specialization. We then show that this phenomenon of jumping geometric genus presents itself in some compact Shimura surfaces. Finally, we find a set of conditions, met by the latter Shimura surfaces, that forces the higher plurigenera to remain constant in reduction modulo p.

Keywords

algebraic surfaceplurigenusmixed characteristic

MSC classification

Secondary: 14L30: Group actions on varieties or schemes (quotients) 14J29: Surfaces of general type 14G35: Modular and Shimura varieties
Type
Research Article
Information
Compositio Mathematica , Volume 144 , Issue 5 , September 2008 , pp. 1214 - 1226
Copyright
Copyright © Foundation Compositio Mathematica 2008