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UID:6c729e02c89e0cad4c1eada92e0bf773
CATEGORIES:Complex Analysis and Geometry Seminar
CREATED:20230904T225647
SUMMARY: Introduction to optimal degeneration problems
LOCATION:Hill 525
DESCRIPTION:Abstract: Optimal degeneration is a 'test configuration' of a projective va
 riety X which degenerates the variety X to a variety Y K-semistable in an e
 xtended 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 importan
 tly it clarifies the right treatment of K-unstable varieties in moduli theo
 ry. \nThere 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 framewor
 k of K-stability for 'spacetime' (relative K-stability, modified D-stabilit
 y, muK-stability, ...). \nI would like to sketch the blueprint of optimal d
 egeneration problem and report where we are now in the long way to go. \n
X-ALT-DESC;FMTTYPE=text/html:<p style="font-size: 11pt; font-family: Calibri, sans-serif; margin: 0px;">
 Abstract: Optimal degeneration is a 'test configuration' of a projective va
 riety X which degenerates the variety X to a variety Y K-semistable in an e
 xtended sense. It is characterized as a maximizer of a certain quantity for
  test configurations. The conjectural&nbsp;existence of optimal degeneratio
 n is important as it completes the proof of the YTD conjecture and more imp
 ortantly it clarifies&nbsp;the right treatment of K-unstable varieties in m
 oduli theory.&nbsp;</p><p style="font-size: 11pt; font-family: Calibri, san
 s-serif; margin: 0px;">There are various frameworks of optimal degeneration
  depending on the choice of the quantity (normalized Donaldson-Futaki invar
 iant, H-entropy, mu-entropy, ...), which corresponds to choosing a certain 
 extended framework of K-stability for 'spacetime' (relative K-stability, mo
 dified D-stability, muK-stability, ...).&nbsp;</p><p style="font-size: 11pt
 ; font-family: Calibri, sans-serif; margin: 0px;">I would like to sketch&nb
 sp;the blueprint of optimal degeneration problem and report&nbsp;where we a
 re now in the long way to go.&nbsp;</p>
CONTACT:Eiji Inoue, RIKEN iTHEMS, Japan
DTSTAMP:20260827T115848
DTSTART;TZID=America/New_York:20230908T103000
DTEND;TZID=America/New_York:20230908T113000
SEQUENCE:0
TRANSP:OPAQUE
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