Degenerations of abelian surfaces and Hodge structures

Details Degenerations of abelian surfaces and Hodge structures Degenerations of abelian surfaces and Hodge structures

1994-04-12

arxiv.org/abs/alg-geom/9404006v2

Schriftenreihe Forschungsschwerpunkt komplexe Mannigfaltigkeiten Heft Nr. 191

Mathematics

Algebraic Geometry

35 pages, AMS-LaTeX 1.1 (amstex,amssymb,amscd,theorem), (revised version: only minor TeX-changes)

Scientific paper

In this paper the authors consider a certain toroidal compactification of the moduli space of degenerations of (1,p)-polarized abelian surfaces with (canonical) level structure. Using Hodge theory we give a proof that a degenerate abelian surface associated to a corank 1 boundary point is (almost) completely determined by the boundary point. The crucial ingredient in the proof is the Local Invariant Cycle theorem which relates the variation of Hodge structure to the mixed Hodge structure on the singular surface.

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