Author : Maria del Rosario Gonzalez-Dorrego
Publisher : American Mathematical Society(RI)
ISBN 13 : 9781470400897
Total Pages : 114 pages
Book Rating : 4.4/5 (8 download)
Book Synopsis 16,6 Configurations and Geometry of Kummer Surfaces in by : Maria del Rosario Gonzalez-Dorrego
Download or read book 16,6 Configurations and Geometry of Kummer Surfaces in written by Maria del Rosario Gonzalez-Dorrego and published by American Mathematical Society(RI). This book was released on 2014-08-31 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.