Asher Auel<br>
Title: Cubic fourfolds containing a plane and a quartic scroll
<br>
Abstract:
Proving the irrationality of the generic complex cubic fourfold
X is a
major open problem in algebraic geometry.  If X contains a
plane, then
there is an associated K3 surface of degree 2 together with a
Brauer
class, called the Clifford invariant of X.  Hassett proved that
if the
Clifford invariant is trivial, then X is rational.  Whether the
converse holds was an open question.  In this talk, I'll speak
about
joint work with Marcello Bernardara, Michele Bolognesi, and
Tony
V?rilly-Alvarado, constructing rational cubic fourfolds
containing a
plane with nontrivial Clifford invariant, thereby showing that
the
converse does not hold.  Our approach uses classical Hodge
theory, as
well as point counting techniques over finite fields, to study
certain
codimension 2 loci in the moduli space of cubic fourfolds.
Finally, I
will spell out the connection to Kuznetsov's derived
categorical
conjecture on the rationality of cubic fourfolds.