Discriminant Quadratic Forms and their Applications to the Classifications of Real K3 Surfaces
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(2) 北海道教育大学紀要（自然科学編）第69巻 第１号 Journal of Hokkaido University of Education（Natural Sciences）Vol. 69, No.1. 平 成 30 年 ８ 月 August, 2018. 判別２次形式とその実K3曲面の分類への応用 齋 藤 幸 子 北海道教育大学教育学部旭川校数学教育専攻. Discriminant Quadratic Forms and their Applications to the Classifications of Real K3 Surfaces SAITO Sachiko Department of Mathematics Education, Asahikawa Campus, Hokkaido University of Education. ABSTRACT In this note we introduce the notion of discriminant quadratic forms of lattices and apply it to the isometric classifications of integral involutions of the K3 lattice with some condition. Such an algebraic classification is the first step to the geometric investigations of real or complex K3 surfaces of some types. We give a detailed explanation of the enumeration of isometry classes of integral involutions of the K3 lattice with condition ((3, 1, 1), -id). Each isometry class is given by a list of genus invariants, and some of these invariants are defined by discriminant quadratic forms of lattices.. 2010 AMS Mathematics Subject Classification: 14J28, 14P25, 14J10.. 9.
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