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Complex Analysis and Geometry Seminar

Introduction to optimal degeneration problems

Eiji Inoue, RIKEN iTHEMS, Japan

Location:  Hill 525
Date & time: Friday, 08 September 2023 at 10:30AM - 11:30AM

Abstract: Optimal degeneration is a 'test configuration' of a projective variety X which degenerates the variety X to a variety Y K-semistable in an extended sense. It is characterized as a maximizer of a certain quantity for test configurations. The conjectural existence of optimal degeneration is important as it completes the proof of the YTD conjecture and more importantly it clarifies the right treatment of K-unstable varieties in moduli theory. 

There are various frameworks of optimal degeneration depending on the choice of the quantity (normalized Donaldson-Futaki invariant, H-entropy, mu-entropy, ...), which corresponds to choosing a certain extended framework of K-stability for 'spacetime' (relative K-stability, modified D-stability, muK-stability, ...). 

I would like to sketch the blueprint of optimal degeneration problem and report where we are now in the long way to go. 

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