Stability of klt singularities

Abstract: A theorem of Donaldson and Sun asserts that the metric tangent cone of a smoothable Kähler–Einstein Fano variety underlies some algebraic structure, and they conjecture that the metric tangent cone only depends on the algebraic structure of the singularity. Later Li and Xu extend this speculation and conjecture that every klt singularity has a canonical “stable” degeneration induced by the valuation that minimizes the normalized volume. I’ll talk about some recent work with Chenyang Xu on the solution of these conjectures. If time permits, I will also discuss some further implications on the boundedness of singularities.

algebraic geometry

Audience: researchers in the topic

Stanford algebraic geometry seminar

Series comments: The seminar was online for a significant period of time, but for now is solely in person. More seminar information (including slides and videos, when available): agstanford.com