Geometric analysis of Chow Mumford stability

By S. Paul. 2004

59 citations recorded by the source corpus.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/ab09873712d6ed0acd78d3b9d96311c7791e5bd5

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In Applied Mathematics

In Geometry and Topology

Citations in the corpus

Blowing up Kähler manifolds with constant scalar curvature, II (2005, result): “Recent years have seen some spectacular works, inspired by the analogy with the Hitchin-Kobayashi correspondence for vector bundles, relating the existence of canonical metrics to dierent stability notions of manifolds [29], [8], [ 21 ], [18].”
Blowing up and desingularizing constant scalar curvature Kähler manifolds (2004, background): “One of the main source of interest in Kähler metrics with constant scalar curvature lies in its relation with algebraic geometric properties of the underlying manifold, such as Chow-Mumford, Tian, or asymptotic Hilbert-Mumford stability (see for example [55], [17], [48], [46], [40]).”
Hyperdiscriminant polytopes, Chow polytopes, and Mabuchi energy asymptotics (2008, unknown): “[29] S.T. Paul.”
The Monge-Ampère operator and geodesics in the space of Kähler potentials (2005, background): “6) The asymptotic behavior of F 0 ωφ0 along geodesics in Hk is known to be closely related to Chow-Mumford stability (see [31], and also [20], [21],[23]).”
Test configurations for K-stability and geodesic rays (2006, background): “Let V be a finite dimensional vector space, Z ⊆ P(V ) a smooth subvariety, and B ∈ gl(V ).”
Multiplier Ideal Sheaves and the K\"ahler-Ricci Flow (2006, unknown): “may be of some practical use, since while the functional Fω0 (φ) decreases along the K¨ahler-Ricci ﬂow, it is the functional F0 ω0 (φ) which is more directly linked to ChowMumford stability (see e.g. [30, 20, 17]). • Since the functional Fω0 (φ) decreases along the K¨ahler-Ricci ﬂow, Fω0 (φ) and hen”
Stability, energy functionals, and Kahler-Einstein metrics (2002, background): “is a vector space of dimension n + 1. The tangent space of ζ at the point x is canonically isomorphic to x⊥ ∩ ζ = ζ� ⊆ CN +1 .L etζ1, ..., ζn be an orthonormal basis of ζ� .L et B(c, x; ζ1, ..., ζn )= P1∗ # M · P ∗”