On the birational geometry of varieties of maximal Albanese dimension

2001/05/09 by C. D. Hacon, Hacon, C. D., R. Pardini +1 · 1 citation
Mathematics · #14J40 14K12 14E05 14K99 #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:14E05 #msc:14J40 #msc:14K12 #msc:14K99

paper · pdf · doi:10.48550/arxiv.math/0105070

Latex file, 28 pages

arxiv created 2001/05/09 · arxiv updated 2009/11/30

Abstract

We study the birational geometry of varieties of maximal Albanese dimension. In particular we discuss criteria for a generically finite morphism of varieties of maximal Albanese dimension to be birational; we give a new characterization of Theta divisors; we study the Albanese map and refine some of the results of Kollár; finally we use these results to birationally classify varieties with P₃(X)=2 and q(X)=dim (X). Our method combines the generic vanishing theorems of Green and Lazarsfeld, the theory of Fourier Mukai transforms and the results of Kollàr on higher direct images of dualizing sheaves.

Cited by

• Generic vanishing theory in positive characteristic

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