The map defined by a non-very ample line bundle on an irregular variety

2011/11/21 by Lei Zhang, Zhang, Lei · 2 citations
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG

paper · pdf · doi:10.48550/arxiv.1111.4798

This paper has been withdrawn by the author. overlapped by axiv:1209.2939, axiv:1210.2060

arxiv created 2014/07/04 · arxiv updated 2014/07/07

Abstract

In this paper, we studied the map defined by a non-very ample line bundle on some special irregular varieties. As to this topic, it is well known that for a line bundle L on an Abelian variety A, the linear system |2L| is base point free, and 3L is very ample, moreover the map defined by the linear system |2L| is well understood (cf. Theorem \refoldth). First, we generalized this classical result to projective bundles over Abelian varieties (cf. Theorem \refkey). Then we studied the bicanonical map of an irregular primitive variety X of general type with dim(X) = q(X), in fact we got a relation between the map and the reducibility of a divisor.

Cited by

• A note on the linear systems on the projective bundles over Abelian varieties
• On the bicanonical maps of primitive varieties with q(X) = dim(X): the degree and the Euler number

Related

• A note on the linear systems on the projective bundles over Abelian varieties
• Peculiar Loci of Ample and Spanned Line Bundles
• On the bicanonical map of irregular varieties
• Symmetry and Variation of Hodge Structures
• On the bicanonical maps of primitive varieties with q(X) = dim(X): the degree and the Euler number