Algebraic tori in the complement of quartic surfaces

Algebraic Geometry Seminar

Organizers：

Caucher Birkar，贾甲

Speaker：

Eduardo Alves da Silva (University of Basel)

Time：

Fri., 15:30-16:30, Dec. 19, 2025

Venue：

B725, Shuangqing Complex Building A

Online：

Zoom Meeting ID: 262 865 5007

Passcode: YMSC

Title:

Algebraic tori in the complement of quartic surfaces

Abstract:

Log Calabi-Yau pairs can be thought of as generalizations of Calabi-Yau varieties. Previously, Ducat showed that all coregularity 0 log Calabi-Yau pairs $(\mathbb{P}^3,B)$ are crepant birational to a toric model. A stronger condition to consider is whether the complement of $B$ contains a dense algebraic torus. When this is the case, we say that the pair $(\mathbb{P}^3,B)$ is of cluster type. In this talk, we will show a complete classification of coregularity 0, semi-log canonical (slc), reducible quartic surfaces whose complements contain a dense algebraic torus. As part of this discussion, we will explore the concept of relative cluster type pairs. Finally, we will share some partial results concerning the case of irreducible quartic surfaces. This work is based on joint research with Fernando Figueroa and Joaquín Moraga.