Varieties with vanishing holomorphic Euler characteristic
Resource
Jour. Reine Angew. Math., 691, (2014), 203-227, arXiv 1105.3418
Journal
Journal fur die Reine und Angewandte Mathematik
Journal Issue
691
Pages
203-227
Date Issued
2014
Author(s)
Abstract
Abstract. We study smooth complex projective varieties X of maximal Albanese dimension and of general type satisfying �q ( X , ? X ) = 0 $\chi (X, \mathcal {O}_X)=0$ . 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 ?tale 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 h 0 ( X , �s X ) = 1 $h^0(X, \omega _X)=1$ . Examples were constructed by Chen and Hacon, and again, we prove that in dimension 3, these examples are (up to abelian ?tale covers) the only ones. We also formulate a conjecture on the general structure of these varieties in all dimensions.
Type
journal article
File(s)![Thumbnail Image]()
Loading...
Name
1105.3418.pdf
Size
354.17 KB
Format
Adobe PDF
Checksum
(MD5):de770e56e540c6057e335da1393a5fbe