A Siegel Modular 3-fold that is a Picard Modular 3-fold

Bruce Hunt
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Bruce Hunt: Universität Kaiserslautern, FB Mathematik

A chapter in Algebraic Geometry, 1990, pp 203-242 from Springer

Abstract: Abstract Let D be a bounded symmetric domain. Г ⊂ Aut( D) be a discrete, properly discontinuous group. If Г is cocompact and acts freely, it has been known for several decades (Kodaira: [K], Hirzebruch: [Hi]) that Г\ D is then an algebraic variety, and in fact of general type. The Hirzebruch proportionality theorem then tells us the (ratios of) Chern numbers of X = Г\ D, which allows us to recover D from the Chern numbers of X if we know only that X is of the form Г\ D for some D. The group Г is then of course just the fundamental group π1(X). So it can’t happen, for example, that X = Г\ D = Г\D′ for 2 non-isomorphic bounded symmetric domains D and D′.

Keywords: Modulus Space; Modular Form; Double Point; Hyperelliptic Curve; Congruence Subgroup (search for similar items in EconPapers)
Date: 1990
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DOI: 10.1007/978-94-009-0685-3_10

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