Back to Algebraic Geometry Seminar: Spring 2023
Algebraic Geometry Seminar
Date: Tuesday, Apr 11, 2023
Time: 3:30PM - 4:30PM
Location: LCB 323
Jennifer Li
Princeton University
Title |
On the cone conjecture for log Calabi-Yau threefolds |
Abstract |
Let ((Y, D)) be a log Calabi-Yau threefold, meaning that (Y) is a smooth projective threefold over (\mathbb{C}) and (D \subset Y) is a normal crossing divisor such that (K_{Y}+D) is trivial. Moreover, suppose that (D) is maximal, meaning there exists a (0)-stratum of (D). Suppose there exists a (K3)-fibration (f: (Y, D) \rightarrow (\mathbb{P}^{1}, \infty)) with (D = f^{\ast}(\infty)) and (H^{3}(Y)=0). Such fibrations arise as mirrors to Fano threefolds. I show that the pseudoautomorphism group of (Y) acts on the codimension one faces of the movable effective cone of (Y) with finitely many orbits. This is implied by the Kawamata-Morrison-Totaro cone conjecture. |
Algebraic Geometry