Cubic fourfolds, K3 surfaces, and rationality questions

Abstract

This is a survey of the geometry of complex cubic fourfolds with a view toward rationality questions. Topics include classical constructions of rational examples, Hodge structures and special cubic fourfolds, associated K3 surfaces and their geometric interpretations, and connections with rationality and unirationality constructions.

arXiv comment37 pages, for the June 2015 CIME-CIRM Course on Rationality Problems in Algebraic Geometry; revision incorporates suggestions from readers and the referee