English

Construction of hyperbolic Horikawa surfaces

Algebraic Geometry 2018-11-20 v2 Complex Variables

Abstract

We construct a Brody hyperbolic Horikawa surface that is a double cover of P2\mathbb{P}^2 branched along a smooth curve of degree 1010. We also construct Brody hyperbolic double covers of Hirzebruch surfaces with branch loci of the lowest possible bidegree.

Keywords

Cite

@article{arxiv.1702.08143,
  title  = {Construction of hyperbolic Horikawa surfaces},
  author = {Yuchen Liu},
  journal= {arXiv preprint arXiv:1702.08143},
  year   = {2018}
}

Comments

16 pages; comments are very welcome. Final version, to appear in Annales de l'Institut Fourier

R2 v1 2026-06-22T18:29:01.500Z