Enriques surfaces with eight nodes

Margarida Mendes Lopes; Rita Pardini

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Enriques surfaces with eight nodes

Margarida Mendes Lopes·Rita Pardini

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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 $\Z_2^2$ or to $\Z_2^3$ acting freely in codimension 1. We use this result to show that if $S$ is a minimal surface of general type with $p_g=0$ such that the image of the bicanonical map is birational to an Enriques surface then $K^2_S=3$ and the bicanonical map is a morphism of degree 2.

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BibTeX RIS

Margarida Mendes Lopes, Rita Pardini. 2001-10-11. Enriques surfaces with eight nodes. https://arxiv.org/abs/math/0110122

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