Back to Algebraic Geometry Seminar: Fall 2023
Algebraic Geometry Seminar
Date: Tuesday, Oct 3, 2023
Time: 3:30PM - 4:30PM
Location: LCB 323
Talon Stark
UCLA
Title |
The cone conjecture in relative dimension 2 |
Abstract |
The Kawamata-Morrison-Totaro cone conjecture concerns the action of automorphisms on the nef effective cone in N^1(X) and pseudo-automorphisms (birational automorphisms that are isomorphisms in codimension 1) on the movable effective cone of divisors. The former classifies contractions, and the latter classifies marked SQMs (roughly, sequences of flops). It began in the 90s as a conjecture of Morrison on Calabi-Yau manifolds, inspired by intuitions from string theory, but has since extended in scope. It predicts that these actions produce only finitely many orbits of faces of the nef effective cone and finitely many chambers of the movable effective cone – hence finitely many orbits/isomorphism classes of contractions and SQMs. This talk will motivate the conjecture, include examples, and build up to current work with Joaquin Moraga where we prove this conjecture for klt log CY fibrations of relative dimension 2. |
Algebraic Geometry