Birational cubic fourfolds via Enriques Cremona transformations

Location: 11th Floor Lecture Hall Speaker Lisa Marquand, Rutgers University Session Chair Sarah Frei, Rice University Abstract The birational geometry of a cubic fourfold is notoriously difficult to study. In particular, birational maps between (conjecturely) irrational cubic fourfolds are few and far between. We focus on the codimension 1 loci of cubic fourfolds containing an Enriques surface. We produce a Cremona transform of P^5, based in a Fano embedded Enriques surface as well as twenty planes. Using this, we produce birational maps between cubic fourfolds containing this surface and their unique Fourier Mukai partners. This is joint work with Corey Brooke.