# 16, 6 Configurations and Geometry of Kummer Surfaces in P3 by Maria R. Gonzalez-Dorrego

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 varied from 2). This Kummer floor is a quartic floor with 16 nodes as its purely singularities. those nodes provide upward thrust to a configuration of 16 issues and 16 planes in ${\mathbb P}^3$ such that every aircraft comprises precisely six issues and every aspect belongs to precisely six planes (this is named a '(16,6) configuration').A Kummer floor is uniquely made up our minds via its set of nodes. Gonzalez-Dorrego classifies (16,6) configurations and experiences their manifold symmetries and the underlying questions on finite subgroups of $PGL_4(k)$. She makes use of this data to provide an entire category 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.