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Geometric Analysis Seminar

WEIGHTED K-STABILITY OF K\”AHLER MANIFOLDS AND EXTREMALITY OF SASAKI MANIFOLDS

Vestislav Apostolov - UQAM

Location:  Zoom
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.