关于不规则簇的双典范映射
代数几何
2009-10-08 v2
摘要
从多典范映射双有理性的统一界来看，一般类型且具有最大阿尔巴尼斯维数的非规则簇的行为类似于曲线。事实上，Chen-Hacon 表明，至少当它们的全纯欧拉示性数为正时，这类簇的三典范映射总是双有理的。在本文中，我们研究双典范映射。我们考虑由阿尔巴尼斯一般类型的本原簇构成的最大阿尔巴尼斯维数簇的自然子类。我们证明，这类簇中唯一具有非双有理双典范映射的是曲线亏格为2这一情形在此语境下的自然高维推广：双有理等价于一个不可分解主极化阿贝尔簇的theta除子的簇。该证明基于（广义）Fourier-Mukai变换。
引用
@article{arxiv.0907.4363,
title = {On the bicanonical map of irregular varieties},
author = {Miguel Angel Barja and Martí Lahoz and Juan Carlos Naranjo and Giuseppe Pareschi},
journal= {arXiv preprint arXiv:0907.4363},
year = {2009}
}
备注
20 pages. There was an inaccuracy in the proof of Theorem 4.13. We have fixed the problem giving a slightly different proof. The modifications only affect to Section 4 of the paper: there is a new definition and we have eliminated a Corollary, which now becomes useless (although it was correct)