Remark on polarized K3 surfaces of genus 36

2010/04/25 by Ilya Karzhemanov, Karzhemanov, Ilya
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #math.AG

paper · pdf · doi:10.48550/arxiv.1004.4343

8 pages; minor corrections, Lemma 4.7 added

openalex publication_date 2010/04/25 · arxiv created 2010/12/16 · arxiv updated 2010/12/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Smooth primitively polarized K3 surfaces of genus 36 are studied. It is proved that all such surfaces S, for which there exists an embedding R \hookrightarrow Pic(S) of some special lattice 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.

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