Seminario Nacional de Geometría Algebraica

Brendan Hassett, Brown University

An algebraic variety is rational if it admits a birational parametrization by affine space. Techniques from Hodge theory and algebraic cycles make it possible to distinguish rational and irrational members in families of smooth projective fourfolds. However, we still do not know precisely which cubic fourfolds are rational! Recent breakthroughs on the irrationality of general cubic fourfolds have sparked new interest in these long-standing questions.

https://www.matem.unam.mx/~lozano/eseminar.html