Download E-books 16, 6 Configurations and Geometry of Kummer Surfaces in P3 (Memoirs of the American Mathematical Society) PDF

By Maria R. Gonzalez-Dorrego

This monograph reviews the geometry of a Kummer floor in ${\mathbb P}^3_k$ and of its minimum desingularization, that's a K3 floor (here $k$ is an algebraically closed box of attribute assorted from 2). This Kummer floor is a quartic floor with 16 nodes as its in basic terms singularities. those nodes supply upward push to a configuration of 16 issues and 16 planes in ${\mathbb P}^3$ such that every airplane comprises precisely six issues and every aspect belongs to precisely six planes (this is termed a '(16,6) configuration').A Kummer floor is uniquely made up our minds by means of its set of nodes. Gonzalez-Dorrego classifies (16,6) configurations and reviews their manifold symmetries and the underlying questions about finite subgroups of $PGL_4(k)$. She makes use of this knowledge to offer a whole class of Kummer surfaces with specific equations and specific descriptions in their singularities. moreover, the attractive connections to the idea of K3 surfaces and abelian types are studied.

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