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WEIGHTED K-STABILITY OF K\”AHLER MANIFOLDS AND EXTREMALITY OF SASAKI MANIFOLDS
Vestislav Apostolov - UQAM
Date & time: Tuesday, 04 May 2021 at 2:50PM - 3:50PM
Abstract: In this talk, I will discuss an equivalence (established in a joint work with D. Calderbank) between extremal Sasaki structures and weighted extremal Kähler metrics in the sense of A. Lahdili. In the case of Sasaki-Einstein structures, this correspondence yields a special case of \(g\)-solitons on a Fano variety, studied by Berman--Witt-Nystr”om and Han--Li. This provides an alternative approach— entirely within the framework of K”ahler geometry— to the K-stability of affine complex cones associated to a Sasaki polarizations, proposed by Collins--Székelyhidi. We will use this and a recent work by He-Li to show that the variational approach to special K”ahler metrics can be applied to prove that extremal Sasaki manifolds are equivariantly K-polystable, thus improving upon the previously known K-semistability.
This talk is based on a joint works with David Calderbank and Eveline Legendre, and Simon Jubert and Abdellah Lahdili, respectively.