A practical algorithm to compute the geometric Picard lattice of K3 surfaces of degree $2$

Dino Festi

A practical algorithm to compute the geometric Picard lattice of K3 surfaces of degree $2$

Algebraic Geometry 2018-10-09 v3

Authors: Dino Festi

Abstract

Let $k$ be either a number a field or a function field over $\mathbb{Q}$ with finitely many variables. We present a practical algorithm to compute the geometric Picard lattice of a K3 surface over $k$ of degree $2$ , i.e., a double cover of the projective plane over $k$ ramified above a smooth sextic curve. The algorithm might not terminate, but if it terminates then it returns a proven correct answer.

Keywords

k3 surfaces geometric picard lattice degree 2 practical algorithm number field function field

Cite

@article{arxiv.1808.00351,
  title  = {A practical algorithm to compute the geometric Picard lattice of K3 surfaces of degree $2$},
  author = {Dino Festi},
  journal= {arXiv preprint arXiv:1808.00351},
  year   = {2018}
}

Comments

A remark about an application of the algorithm to quartc surfaces with a node. Proposition 5.1 corrected. Acknowledgements and bibliography updated. Few typos corrected. 14 pages, 1 figure. Comments still welcome!

A practical algorithm to compute the geometric Picard lattice of K3 surfaces of degree $2$

Abstract

Keywords

Cite

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