Algebraic Geometry Seminar
Lisa Marquand
New York University
Cubic fourfolds with birational Fano varieties of lines
Abstract: Cubic fourfolds have been classically studied up to birational
equivalence, with an eye towards rationality problems. On the
other hand, the Fano variety of lines F(X) on a cubic fourfold X
is a hyperkahler manifold, and the rationality/irrationality of
X is conjecturely reflected in the geometry of the Fano variety
of lines. We give examples of conjecturally irrational cubic
fourfolds with birationally equivalent Fano varieties of lines.
Two of our examples, which are special families in C_12, provide
new examples of pairs of cubic fourfolds with equivalent Kuznetsov
components. Further, we show the cubic fourfolds themselves are
birational. Our examples were discovered by studying the group of
birational transformations of the Fano varieties of lines of these
cubic fourfolds. This is joint work with Corey Brooke and Sarah Frei,
building on our previous work with Xuqiang Qin.
Monday March 10, 2025 at 3:00 PM in 636 SEO