On Mumford's construction of degenerating abelian varieties

Details On Mumford's construction of degenerating abelian varieties On Mumford's construction of degenerating abelian varieties

1996-08-17

arxiv.org/abs/alg-geom/9608014v2

Mathematics

Algebraic Geometry

Final version, to appear in Tohoku Math. J

Scientific paper

We prove that a 1-dimnl family of abelian varieties with an ample sheaf defining principal polarization can be canonically compactified (after a finite base change) to a projective family with an ample sheaf. We show that the central fiber (P,L), which we call an SQAV, has a canonical Cartier theta divisor. We give a combinatorial definition for SQAVs and describe their geometrical properties, in particular compute cohomologies of L^n, n\ge0.

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