The dihedral group \Dh₅ as group of symplectic automorphisms on K3 surfaces

2008/12/24 by Alice Garbagnati, Garbagnati, Alice
Mathematics · #14J28 #14J50 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #math.AG #msc:14J28 #msc:14J50

paper · pdf · doi:10.48550/arxiv.0812.4518

11 pages. Arguments revised, results unchanged. Final version, to appear in Proc. Amer. Math. Soc

openalex publication_date 2008/12/24 · arxiv created 2010/07/07 · arxiv updated 2010/07/08 · openalex created_date 2022/09/12 · openalex updated_date 2026/07/28

Abstract

We prove that if a K3 surface X admits \Z/5\Z as group of symplectic automorphisms, then it actually admits \Dh₅ as group of symplectic automorphisms. The orthogonal complement to the \Dh₅-invariants in the second cohomology group of X is a rank 16 lattice, L. It is known that L does not depend on X: we prove that it is isometric to a lattice recently described by R. L. Griess Jr. and C. H. Lam. We also give an elementary construction of L.

Citations

• EE₈-lattices and dihedral groups

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