Regularity on abelian varieties II: basic results on linear series and defining equations

Details Regularity on abelian varieties II: basic results on linear series and defining equations Regularity on abelian varieties II: basic results on linear series and defining equations

2001-09-28

arxiv.org/abs/math/0110004v2

J. Alg. Geom. 13 (2004), 167-193

Mathematics

Algebraic Geometry

22 pages; mistake in Example 3.7 and a few typos corrected; final version to appear in J. Algebraic Geom

Scientific paper

This paper is mainly concerned with applying the theory of M-regularity developed in the previous math.AG/0110003 to the study of linear series given by multiples of ample line bundles on abelian varieties. We define a new invariant of a line bundle, called M-regularity index, which is seen to govern the higher order properties and (partly conjecturally) the defining equations of such embeddings. We prove a general result on the behavior of higher syzygies in embeddings given by multiples of ample bundles whose base locus has no fixed components, extending a conjecture of Lazarsfeld known to be true by work of the first author. This approach also unifies essentially all the previously known results in this direction and is mainly based on vanishing theorems rather than representations of theta groups.

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