Surfaces on the Severi line

Miguel Ángel Barja; Rita Pardini; Lidia Stoppino

Surfaces on the Severi line

Algebraic Geometry 2022-08-09 v1

Authors: Miguel Ángel Barja , Rita Pardini , Lidia Stoppino

Abstract

Let S be a minimal complex surface of general type and of maximal Albanese dimension; by the Severi inequality one has $K^2_S\geq 4\chi(\mathcal O_S)$ . We prove that the equality $K^2_S=4\chi(\mathcal O_S)$ holds if and only if $q(S):= h^1(\mathcal O_S)=2$ and the canonical model of $S$ is a double cover of the Albanese surface branched on an ample divisor with at most negligible singularities.

Keywords

del pezzo surfaces algebraic surfaces minimal surfaces

Cite

@article{arxiv.1504.06590,
  title  = {Surfaces on the Severi line},
  author = {Miguel Ángel Barja and Rita Pardini and Lidia Stoppino},
  journal= {arXiv preprint arXiv:1504.06590},
  year   = {2022}
}

Comments

13 pages

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