Explore a 44-minute lecture on rational cubic fourfolds containing Veronese surfaces, presented by Yu Wei Fan from the University of California at Berkeley. Delve into the study of birational automorphisms induced by Veronese surfaces in P^5 and their impact on cubic fourfolds. Learn about a newly discovered non-trivial birational involution on the space of cubic fourfolds containing a Veronese surface, and its implications for proving rationality of certain cubic fourfolds. Examine the relationship between cubic fourfolds sharing the same K3 category and the Cremona transformation. Follow the speaker's journey through special cubic fourfolds, the Kuznetsov component, rationality conjecture, and the main ideas behind cubic fourfolds containing Veronese surfaces. Gain insights into the involution on C20, Mukai lattice, derived Torelli, transcendental lattices, and blowup formula. Explore algebraic lattices and Fourier-Mukai partners of Ax, culminating in the discovery of new rational cubic fourfolds.
On Rational Cubic Fourfolds Containing Veronese Surfaces
Overview
Syllabus
Intro
Special cubic fourfolds
Kuznetsov component and rationality conjecture
Main idea
Cubic fourfolds containing a Veronese surface
An involution on C20 Proposition
Main Theorem (0)
Ingredients for proving AxAX
Mukai lattice and derived Torelli
Transcendental lattices and blowup formula
Sketch of proof: Ax Ax
Idea of proving X X
Algebraic lattices
Sketch of proof: XXX Proposition
Sketch of proof: Fourier-Mukai partners of Ax (cont'd)
Main Theorem (II): New rational cubic fourfolds
Taught by
IMSA
