On the cone conjecture for log Calabi-Yau mirrors of Fano 3-folds

Abstract: Let $Y$ be a smooth projective 3-fold admitting a K3 fibration $f: Y \rightarrow \mathbb{P}^{1}$ with $-K_{Y} = f^{\ast} \mathcal{O}(1)$. We show that the pseudoautomorphism group of $Y$ acts with finitely many orbits on the codimension one faces of the movable cone if $H^{3}(Y, \mathbb{C}) = 0$, confirming a special case of the Kawamata-Morrison-Totaro cone conjecture. In Coates-Corti-Galkin-Kasprzyk 2016, Przyjalkowski 2018, and Cheltsov-Przyjalkowski 2018, the authors construct log Calabi-Yau 3-folds with K3 fibrations satisfying the hypotheses of our theorem as the mirrors of Fano 3-folds.

algebraic geometrycombinatorics

Audience: researchers in the topic

Online Nottingham algebraic geometry seminar

Series comments: Online geometry seminar, typically held on Thursday. This seminar takes place online via Microsoft Teams on the Nottingham University "Algebraic Geometry" team.

For recordings of past talks, copies of the speaker's slides, or to be added to the Team, please visit the seminar homepage at: kasprzyk.work/seminars/ag.html