12 rational curves on Enriques surfaces
arXiv:2005.12939
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.
v2: 18 pages; typos corrected, arguments in sections 3, 4 expanded