166 Configurations And Geometry Of Kummer Surfaces In Mathbb P3
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16,6 Configurations and Geometry of Kummer Surfaces in
Author | : Maria del Rosario Gonzalez-Dorrego |
Publisher | : American Mathematical Society(RI) |
Total Pages | : 114 |
Release | : 2014-08-31 |
Genre | : MATHEMATICS |
ISBN | : 9781470400897 |
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This monograph studies the geometry of a Summer surface in P ]3 and of its minimal desingularization, which is a K3 surface (here k is an algebraically closed field of characteristic different from 2). This Kummer surface is a quartic surface with sixteen nodes as its only singularities. These nodes give rise to a configuration of sixteen points and sixteen planes in P ]3 such that each plane contains exactly six points and each point belongs to exactly six planes (this is called a (16, 6) configuration). A Kummer surface is uniquely determined by its set of nodes. Gonzalez_Dorrego classifies (16, 6) configurations and studies their manifold symmetries and the underlying questions about finite subgroups of PGL [4 ( k ). She uses this information to give a complete classification of Kummer surfaces with explicit equations and explicit descriptions of their singularities. In addition, the beautiful connections to the theory of K3 surfaces and abelian varieties are studied.
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