Singular and smooth varieties in the minimal model program for threefolds

by Prof. Andreas Höring (University Côte d'Azur), Prof. Donghyeon Kim (Yonsei University)

Thursday 22 May 2025, 09:00 → 11:00 Europe/Paris

Thursday 22 May 2025, 4:00 PM - 6:00 PM (Korea)

Given a smooth projective surface, running an MMP is simply a sequence of blowdowns of (−1)-curves, so the outcome remains a smooth projective surface. In contrast, for a smooth projective threefold, the outcome of the MMP can be singular. It is well known that the MMP improves singularities in the sense of the minimal model program. But singularities in the sense of smoothness may get worse. In particular, Benveniste proved in 1985 that there is no flipping contraction starting with smooth projective threefold, and thus for any Fano-type threefold X with −K_X movable, a −K_X-MMP does not result in any smooth varieties except for X itself.

In the first part of this talk, we will recall the basics of the MMP and illustrate key examples of these phenomena.

In the second part, we will discuss how to gain additional control over singularities when running an MMP starting from a Fano threefold.

LINK FOR THE WEBINAR

https://cnrs.zoom.us/j/99809114553?pwd=QBsnIaRBLtIvpHR8dJHlH7VE6d1XTm.1