Quicklists
Javascript must be enabled

Howie Nuer : Cubic fourfolds containing some classical surfaces, Kuznetsovs conjecture, and the Kodaira dimension of some C_d

root

71 Views

(Special) Cubic fourfolds have garnered a lot of interest lately, most notably because of the difficulty posed by determining their (ir)rationality. We provide explicit descriptions of the generic members of Hassett's divisors C_30, C_38, and C_44 in terms of Fano models of Enriques surfaces and (deformations of) Coble surfaces, and we will use these descriptions to prove the unirationality of these Noether-Lefschetz divisors. After placing this result in the context of a Gritsenko-Hulek-Sankaran-type result and time permitting, we will go on to further enumerate the 13 irreducible components of C_8 \cap C_44 and describe some of them in terms of the rich geometry of Enriques surfaces. In doing so, we describe 7 new components parametrizing cubic fourfolds with trivial Clifford invariant, which are thus rational and verify Kuznetsov's conjecture. Another 6 components have nontrivial Clifford invariant and could provide new nontrivial examples of Kuznetsov's conjecture. This is a work-in-progress.

Please select playlist name from following

Report Video

Please select the category that most closely reflects your concern about the video, so that we can review it and determine whether it violates our Community Guidelines or isn’t appropriate for all viewers. Abusing this feature is also a violation of the Community Guidelines, so don’t do it.

0 Comments

Comments Disabled For This Video