Shimura Varieties, Kummer Varieties, and Rational Curves
Algebraic Geometry
2020-09-03 v1
Abstract
For a very general product of seven or more elliptic curves, every rational curve on the Kummer variety of projects trivially onto the Kummer variety of at least one of its factors. As a consequence, a very general member of certain families of abelian varieties parametrized by connected Shimura varieties of unitary type has the property that its Kummer variety has no rational curves.
Cite
@article{arxiv.2009.01128,
title = {Shimura Varieties, Kummer Varieties, and Rational Curves},
author = {Bo-Hae Im and Michael Larsen and Sailun Zhan},
journal= {arXiv preprint arXiv:2009.01128},
year = {2020}
}
Comments
13 pages