K-stability of CY fibrations over curves

Abstract: 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 results.

algebraic geometryanalysis of PDEsalgebraic topologycomplex variablesdifferential geometrygeneral topologygeometric topologyK-theory and homologymetric geometrysymplectic geometry

Audience: researchers in the topic

CRM - Séminaire du CIRGET / Géométrie et Topologie

Series comments: Hybrid seminar of geometry and topology. Laboratory : CIRGET - www.cirget.uqam.ca The homepage of the seminar is www.cirget.uqam.ca/fr/seminaires.html

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