K-Semistability for irregular Sasakian manifolds

2012/04/10 by Collins, Tristan C., Székelyhidi, Gábor · 4 citations
#Algebraic Geometry (math.AG) #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th)

paper · doi:10.48550/arxiv.1204.2230

Abstract

We introduce a notion of K-semistability for Sasakian manifolds. This extends to the irregular case the orbifold K-semistability of Ross-Thomas. Our main result is that a Sasakian manifold with constant scalar curvature is necessarily K-semistable. As an application, we show how one can recover the volume minimization results of Martelli-Sparks-Yau, and the Lichnerowicz obstruction of Gauntlett-Martelli-Sparks-Yau from this point of view.

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• K-polystability of Asymptotically Conical Kähler-Ricci Shrinkers
• The CR Yamabe invariant and constant scalar curvature Sasaki metrics
• Examples of complete Calabi--Yau metrics on affine smoothings of irregular toric Calabi--Yau cones
• On Sun-Zhang's theory of Fano fibrations -- weighted volumes, moduli and bubbling Fano fibrations

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