Varieties with vanishing holomorphic Euler characteristic
Résumé
We study smooth complex projective varieties X of maximal Albanese dimension and of general type satisfying χ(X, OX ) = 0. We prove that the Albanese variety of X has at least three simple factors. Examples were constructed by Ein and Lazarsfeld, and we prove that in dimension 3, these examples are (up to abelian ´etale covers) the only ones. By results of Ueno, another source of examples is provided by varieties X of maximal Albanese dimension and of general type satisfying h0(X, KX ) = 1. Examples were constructed by Chen and Hacon, and again, we prove that in dimension 3, these examples are (up to abelian ´etale covers) the only ones. We also formulate a conjecture on the general structure of these varieties in all dimensions.
Domaines
Géométrie algébrique [math.AG]
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