16, 6 Configurations and Geometry of Kummer Surfaces in P3

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This monograph studies the geometry of a Summer surface in P³ 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 P³ 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.