We provide a new construction of rationality for cubic fourfolds via Mori's theory and the minimal model program. As an application we present the solution of the Kuznetsov conjecture for d = 42 (the first open case). Our methods also show an explicit connection between the ratio-nality of cubic fourfolds belonging to the first four admissible families Cd with d = 14, 26, 38, and 42 and some birational models of K3 surfaces of degree d contained in well known rational Fano fourfolds.

Trisecant flops, their associated K3 surfaces and the rationality of some cubic fourfolds

Russo, F
;
Staglianò, G
2023-01-01

Abstract

We provide a new construction of rationality for cubic fourfolds via Mori's theory and the minimal model program. As an application we present the solution of the Kuznetsov conjecture for d = 42 (the first open case). Our methods also show an explicit connection between the ratio-nality of cubic fourfolds belonging to the first four admissible families Cd with d = 14, 26, 38, and 42 and some birational models of K3 surfaces of degree d contained in well known rational Fano fourfolds.
2023
Rationality of cubic fourfolds
flops
Mori theory
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11769/586893
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus ND
  • ???jsp.display-item.citation.isi??? 2
social impact