12 rational curves on Enriques surfaces
Algebraic Geometry
2021-04-08 v2
Abstract
Given d in IN, we prove that any polarized Enriques surface (over any field of characteristic different from 2 or with a smooth K3 cover) of degree greater than 12d^2 contains at most 12 rational curves of degree at most d. For d>2 we construct examples of Enriques surfaces of high degree that contain exactly 12 rational degree d curves.
Cite
@article{arxiv.2005.12939,
title = {12 rational curves on Enriques surfaces},
author = {Sławomir Rams and Matthias Schütt},
journal= {arXiv preprint arXiv:2005.12939},
year = {2021}
}
Comments
v2: 18 pages; typos corrected, arguments in sections 3, 4 expanded