Note on a family of surfaces with $p_g=q=2$ and $K^2=7$

Matteo Penegini; Roberto Pignatelli

Note on a family of surfaces with $p_g=q=2$ and $K^2=7$

Algebraic Geometry 2021-07-01 v3

Authors: Matteo Penegini , Roberto Pignatelli

Abstract

We study a family of surfaces of general type with $p_g=q=2$ and $K^2=7$ , originally constructed by C. Rito. We provide an alternative construction of these surfaces, that allows us to describe their Albanese map and the corresponding locus $\mathcal{M}$ in the moduli space of the surfaces of general type. In particular we prove that $\mathcal{M}$ is an open subset, and it has three connected components, two dimensional, irreducible and generically smooth.

Keywords

surfaces of general type albanese map moduli space pg=q=2 k2=7 rito construction

Cite

@article{arxiv.2012.05636,
  title  = {Note on a family of surfaces with $p_g=q=2$ and $K^2=7$},
  author = {Matteo Penegini and Roberto Pignatelli},
  journal= {arXiv preprint arXiv:2012.05636},
  year   = {2021}
}

Comments

26 pages, 7 figures. In this version we have corrected a miscalculation of the previous version regarding the number of components

Note on a family of surfaces with $p_g=q=2$ and $K^2=7$

Abstract

Keywords

Cite

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