Remark on polarized K3 surfaces of genus 36

Ilya Karzhemanov

Remark on polarized K3 surfaces of genus 36

Algebraic Geometry 2010-12-17 v2

Authors: Ilya Karzhemanov

Abstract

Smooth primitively polarized $\mathrm{K3}$ surfaces of genus 36 are studied. It is proved that all such surfaces $S$ , for which there exists an embedding $\mathrm{R} \hookrightarrow \mathrm{Pic}(S)$ of some special lattice $\mathrm{R}$ of rank 2, are parameterized up to an isomorphism by some 18-dimensional unirational algebraic variety. More precisely, it is shown that a general $S$ is an anticanonical section of a (unique) Fano 3-fold with canonical Gorenstein singularities.

Keywords

K3 surfaces genus 36 polarization Fano 3-fold Gorenstein singularities unirational variety

Cite

@article{arxiv.1004.4343,
  title  = {Remark on polarized K3 surfaces of genus 36},
  author = {Ilya Karzhemanov},
  journal= {arXiv preprint arXiv:1004.4343},
  year   = {2010}
}

Comments

8 pages; minor corrections, Lemma 4.7 added

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