English

Enriques surfaces with eight nodes

Algebraic Geometry 2007-05-23 v1

Abstract

A nodal Enriques surface can have at most 8 nodes. We give an explicit description of Enriques surfaces with 8 nodes, showing that they are quotients of products of elliptic curves by a group isomorphic to Z22\Z_2^2 or to Z23\Z_2^3 acting freely in codimension 1. We use this result to show that if SS is a minimal surface of general type with pg=0p_g=0 such that the image of the bicanonical map is birational to an Enriques surface then KS2=3K^2_S=3 and the bicanonical map is a morphism of degree 2.

Keywords

Cite

@article{arxiv.math/0110122,
  title  = {Enriques surfaces with eight nodes},
  author = {Margarida Mendes Lopes and Rita Pardini},
  journal= {arXiv preprint arXiv:math/0110122},
  year   = {2007}
}

Comments

Latex 2e, 11 pages