Surfaces with $\chi=5, K^{2}=9$ and a canonical involution

Zhiming Lin

Surfaces with $\chi=5, K^{2}=9$ and a canonical involution

Algebraic Geometry 2016-06-21 v1

Authors: Zhiming Lin

Abstract

In this paper, we classify the minimal surfaces of general type with $\chi=5$ , $K^{2}=9$ whose canonical map is composed with an involution. We obtain 6 families, whose dimensions in the moduli space are 28, 27, 33, 32, 31 and 32 respectively. Among them, the family of surfaces having a genus 2 fibration forms an irreducible component of $\mathfrak{M}_{\chi=5, K^{2}=9}$ .

Keywords

del pezzo surfaces

Cite

@article{arxiv.1606.05932,
  title  = {Surfaces with $\chi=5, K^{2}=9$ and a canonical involution},
  author = {Zhiming Lin},
  journal= {arXiv preprint arXiv:1606.05932},
  year   = {2016}
}

Comments

18 pages. arXiv admin note: text overlap with arXiv:math/0603094 by other authors

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