Relative K-stability of extremal metrics

By J. Stoppa, G'abor Sz'ekelyhidi. 2009

55 citations recorded by the source corpus.

We show that if a polarised manifold admits an extremal metric then it is Kpolystable relative to a maximal torus of automorphisms.

Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/d998de7a8718bcf0914cf17e8babd26d0e11e1e4

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Kähler metrics with constant weighted scalar curvature and weighted K‐stability (2018, methodology): “Using a blowup technique and the glueing theorem of Arezzo–Pacard–Singer [8], Stoppa [76] and Stoppa–Székelyhidi [78] have shown that the existence of a cscK or extremal Kähler metric in 2πc1(L) does actually imply (1,wex)-K-stability relative to T, i.”
Extremal K\"ahler metrics (2014, background): “As a consequence of work of Tian [54], Donaldson [18, 20], Mabuchi [34], Stoppa [44], Stoppa-Székelyhidi [45], Paul [39], Berman [7], and others, there are now many satisfactory results that show that the existence of an extremal metric implies various notions of stability.”
Extremal Kähler metrics on projective bundles over a curve (2009, background): “e pair (M,L) — which is the same as the reduced automorphism group Autg 0(M,J) — and the similar implication ‘extremal ⇒ relatively K-polystable’ was recently established by G. Sz´ekelyhidi–J. Stoppa [65]. The Yau–Tian–Donaldson conjecture was inspired by and can be regarded as a nonlinear counterpa”
On blowing up extremal Kähler manifolds (2010, methodology): “emma follows from the KempfNess theorem. Finally we give the proof of Corollary 7. Proof of Corollary 7. We will prove the following three implications. (i)⇒(ii) This follows from the main theorem in [30]. (ii)⇒(iii) This follows from Theorem 5, even though we are using a more restrictive version of”
The complex Monge–Ampère equation on compact Kähler manifolds (2010, background): “e in the class [ω] if and only if (M,L) is K-stable. This is a core problem in Ka¨hler geometry. Thorough the eﬀorts of many mathematicians, the necessary part of this conjecture is essentially done ([50, 23, 26, 17, 41, 47, 48] ). The core problem is to ﬁnd a way to understand existence problem. Ba”
K-polystability of Q-Fano varieties admitting Kähler-Einstein metrics (2012, background): “The case when Aut(X)0 is non-trivial leads to highly non-trivial complications, related to the case when DF = 0 and was treated by Mabuchi in a series of papers [44, 45] (see also [68] where it is shown that if c1(L) contains an extremal Kähler metric, then (X,L) is K-polystable with respect to all ”