• Corpus ID: 235377406

Mutual Asymptotic Fekete Sequences

@inproceedings{Hultgren2021MutualAF,
  title={Mutual Asymptotic Fekete Sequences},
  author={Jakob Hultgren},
  year={2021}
}
A sequence of point configurations on a compact complex manifold is asymptotically Fekete if it is close to maximizing a sequence of Vandermonde determinants. These Vandermonde determinants are defined by tensor powers of a Hermitian ample line bundle and the point configurations in the sequence possess good sampling properties with respect to sections of the line bundle. In this paper, given a collection of toric Hermitian ample line bundles, we give necessary and sufficient condition for… 
1 Citations
Extremal potentials and equilibrium measures associated to collections of K\"ahler classes
Given a collection of Kähler forms and a continuous weight on a compact complex manifold we show that it is possible to define natural new notions of extremal potentials and equilibrium measures

References

SHOWING 1-10 OF 17 REFERENCES
Fekete points and convergence towards equilibrium measures on complex manifolds
Building on [BB1] we prove a general criterion for convergence of (possibly singular) Bergman measures towards pluripotential-theoretic equilibrium measures on complex manifolds. The criterion may be
Equidistribution estimates for Fekete points on complex manifolds
We study the equidistribution of Fekete points in a compact complex manifold. These are extremal point configurations defined through sections of powers of a positive line bundle. Their
Growth of balls of holomorphic sections and energy at equilibrium
Let L be a big line bundle on a compact complex manifold X. Given a non-pluripolar compact subset K of X and a continuous Hermitian metric e−φ on L, we define the energy at equilibrium of (K,φ) as
Equidistribution of Fekete Points on the Sphere
Fekete points are the points that maximize a Vandermonde-type determinant that appears in the polynomial Lagrange interpolation formula. They are well-suited points for interpolation formulas and
Scalar Curvature and Projective Embeddings, I
We prove that a metric of constant scalar curvature on a polarised Kahler manifold is the limit of metrics induced from a specific sequence of projective embeddings; satisfying a condition introduced
Extremal potentials and equilibrium measures associated to collections of K\"ahler classes
Given a collection of Kähler forms and a continuous weight on a compact complex manifold we show that it is possible to define natural new notions of extremal potentials and equilibrium measures
Statistical mechanics of permanents, real-Monge-Ampere equations and optimal transport
We give a new probabilistic construction of solutions to real Monge-Amp\`ere equations in R^n satisfying the second boundary value problem with respect to a given target convex body P) which fits
Large Deviations for Gibbs Measures with Singular Hamiltonians and Emergence of Kähler–Einstein Metrics
In the present paper and the companion paper (Berman, Kähler–Einstein metrics, canonical random point processes and birational geometry. arXiv:1307.3634, 2015) a probabilistic
Permanental Point Processes on Real Tori, Theta Functions and Monge–Ampère Equations
— Inspired by constructions in complex geometry we introduce a thermodynamic framework for Monge–Ampère equations on real tori. We show convergence in law of the associated point processes and
Permanental Point Processes on Real Tori
The main motivation for this thesis is to study real Monge-Ampere equations. These are fully nonlinear differential equations that arise in differential geometry. They lie at the heart of optimal
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