The effective cone conjecture for Calabi--Yau pairs

verfasst von

Cécile Gachet, Hsueh-Yung Lin, Isabel Stenger, Long Wang

Abstract

We formulate an {\it effective cone conjecture} for klt Calabi--Yau pairs (X,Δ), pertaining to the structure of the cone of effective divisors Eff(X) modulo the action of the subgroup of pseudo-automorphisms PsAut(X,Δ). Assuming the existence of good minimal models in dimension dim(X), known to hold in dimension up to 3, we prove that the effective cone conjecture for (X,Δ) is equivalent to the Kawamata--Morrison--Totaro movable cone conjecture for (X,Δ). As an application, we show that the movable cone conjecture unconditionally holds for the smooth Calabi--Yau threefolds introduced by Schoen and studied by Namikawa, Grassi and Morrison. We also show that for such a Calabi--Yau threefold X, all of its minimal models, apart from X itself, have rational polyhedral nef cones.

Organisationseinheit(en)

Institut für Algebraische Geometrie
Riemann Center for Geometry and Physics

Typ

Preprint

Publikationsdatum

11.06.2024

Publikationsstatus

Elektronisch veröffentlicht (E-Pub)