Commutative Algebra and Algebraic Geometry: The Fellowship of the Ring: Syzygies of K3 carpets and Green's conjecture
Seminar | September 10 | 3:45-4:45 p.m. | 939 Evans Hall
Steven Sam, UC San Diego
K3 carpets are double structures on rational normal scrolls. We prove a vanishing statement for their graded Betti numbers which confirms a conjecture of Bayer and Eisenbud for the Betti numbers of ribbon curves. This gives a new proof that Green's conjecture on Betti numbers of canonical curves holds for a generic curve in each gonality stratum of the moduli of curves. This is joint work with Claudiu Raicu.