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The modularity of K3 surfaces with non-symplectic group actions

✍ Scribed by Ron Livné; Matthias Schütt; Noriko Yui

Publisher
Springer
Year
2010
Tongue
English
Weight
270 KB
Volume
348
Category
Article
ISSN
0025-5831

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Classification of non-symplectic automor
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In this paper, we study non-symplectic automorphisms of order 3 on algebraic K3 surfaces over C which act trivially on the Néron-Severi lattice. In particular we shall characterize their fixed loci in terms of the invariants of 3-elementary lattices.

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Given a quadratic extension L/K of fields and a regular alternating space V f of finite dimension over L, we classify K-subspaces of V which do not split into the orthogonal sum of two proper K-subspaces. This allows one to determine the orbits of the group Sp L V f in the set of K-subspaces of V .