Classification of Bagnera-de Franchis Varieties in Small Dimensions

Andreas Demleitner

Classification of Bagnera-de Franchis Varieties in Small Dimensions

Algebraic Geometry 2017-11-27 v3

Authors: Andreas Demleitner

Abstract

A Bagnera-de Franchis variety $X = A/G$ is the quotient of an abelian variety $A$ by a free action of a finite cyclic group $G \subset Bihol(A)$ , which does not contain only translations. Constructing explicit polarizations and using a method introduced by F. Catanese, we classify split Bagnera-de Franchis varieties up to complex conjugation in dimensions $\leq 4$ .

Keywords

Bagnera-de Franchis varieties abelian varieties finite cyclic group polarization complex conjugation classification

Cite

@article{arxiv.1604.07678,
  title  = {Classification of Bagnera-de Franchis Varieties in Small Dimensions},
  author = {Andreas Demleitner},
  journal= {arXiv preprint arXiv:1604.07678},
  year   = {2017}
}

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20 pages

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