Back to Departmental Colloquium: Spring 2017
Departmental Colloquium
Date: Thursday, Mar 9, 2017
Time: 4:00PM
Location: JWB 335
Fabrizio Catanese
Universität Bayreuth
Title |
Configurations of lines and interesting algebraic surfaces |
Abstract |
Many important questions in the theory of surfaces and in algebraic geometry have been solved thanks to explicit constructions of algebraic surfaces as abelian coverings branched over special configurations of lines. After recalling the classical configurations (Pappus, Desargues, Fano, Hesse) and some new ones, I shall describe simple equations for such surfaces, as the Fermat, and Hirzebruch-Kummer coverings. As the configuration of lines becomes special some interesting geometry shows up, as in the case of the six lines of a complete quadrangle, related to the Del Pezzo surface of degree 5 and its icosahedral symmetry. After mentioning many important such examples and applications, by several authors, I shall concentrate on a recent simple series of such surfaces, studied in my joint work with Ingrid Bauer and Michael Dettweiler, discussing new results and quite general open questions, concerning rigid compact complex manifolds, and projective classifying spaces. |
Algebraic Geometry
Commutative Algebra
Topology