New surfaces with $K^2=7$ and $p_g=q\leq 2$

Carlos Rito

New surfaces with $K^2=7$ and $p_g=q\leq 2$

Algebraic Geometry 2017-03-24 v2

Authors: Carlos Rito

Abstract

We construct smooth minimal complex surfaces of general type with $K^2=7$ and: $p_g=q=2,$ Albanese map of degree $2$ onto a $(1,2)$ -polarized abelian surface; $p_g=q=1$ as a double cover of a quartic Kummer surface; $p_g=q=0$ as a double cover of a numerical Campedelli surface with $5$ nodes.

Keywords

complex surfaces of general type minimal surfaces Albanese map polarized abelian surface Kummer surface Campedelli surface double cover

Cite

@article{arxiv.1506.09117,
  title  = {New surfaces with $K^2=7$ and $p_g=q\leq 2$},
  author = {Carlos Rito},
  journal= {arXiv preprint arXiv:1506.09117},
  year   = {2017}
}

Comments

Exposition improved according to Referees' comments. Final version

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