Séminaire CIRGET: «K-stability of CY fibrations over curves»

Conférencier: Masafumi Hattori (Kyoto University)

In K-stability, the characterization of K-stable varieties is well-studied when K_X is ample or X is a Calabi-Yau or Fano variety. However, K-stability of Fano fibrations or Calabi-Yau fibrations (i.e., K_X is relatively trivial) is not known much in algebraic geometry. On the other hand, cscK problems on fibrations are studied by Fine, Jian-Shi-Song and Dervan-Sektnan in Kahler geometry. We introduce adiabatic K-stability (If f:(X,H)\to (B,L) is a fibration of polarized varieties, this means that K-stability of (X,aH+L) for sufficiently small a) and show that adiabatic K-semistability of Calabi-Yau fibration implies log-twisted K-semistability of the base variety by applying the canonical bundle formula and the result on J-stability. If the base is a curve, we also obtain a partial converse. In this talk, I would like to explain our main 

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vendredi 22 septembre 2023
11 h

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UQAM - Pavillon Président-Kennedy (PK)
PK-5115 et en ligne
201, avenue du Président-Kennedy
Montréal (QC)

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