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Characterization of products of theta divisors
- Part of
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- Journal:
- Compositio Mathematica / Volume 150 / Issue 8 / August 2014
- Published online by Cambridge University Press:
- 30 June 2014, pp. 1384-1412
- Print publication:
- August 2014
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- Article
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We study products of irreducible theta divisors from two points of view. On the one hand, we characterize them as normal subvarieties of abelian varieties such that a desingularization has holomorphic Euler characteristic
$\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}1$. On the other hand, we identify them up to birational equivalence among all varieties of maximal Albanese dimension. We also describe the structure of varieties 
$X$ of maximal Albanese dimension, with holomorphic Euler characteristic 
$1$ and irregularity 
$2\dim X-1$.
