Fourier–Mukai Transforms, Euler–Green Currents, and K-Stability

@article{Paul2020FourierMukaiTE,
  title={Fourier–Mukai Transforms, Euler–Green Currents, and K-Stability},
  author={Sean Timothy Paul and Kyriakos Sergiou},
  journal={Geometric Analysis},
  year={2020}
}
Inspired by Gang Tian’s work in [4, 10, 11], and [12] we exhibit a wide range of energy functionals in Khler geometry as Fourier–Mukai transforms. Consequently these energies are completely determined by dual type varieties and therefore have logarithmic singularities when restricted to the space of algebraic potentials. This paper is dedicated to Gang Tian on the occasion of his 60th birthday. 
1 Citations

Faltings Heights, Igusa Local Zeta Functions, and the Stability Conjectures in Kahler Geometry I

Let (X,L) be a polarized manifold. Assume that the automorphism group is finite. If the height discrepancy of (X,L) is O(d^2) then (X,L) admits a csck metric in the first chern class of L if and only

References

SHOWING 1-10 OF 20 REFERENCES

Complex Immersions and Arakelov Geometry

In this paper we establish an arithmetic Riemann-Roch-Grothendieck Theorem for immersions. Our final formula involves the Bott-Chern currents attached to certain holomorphic complexes of Hermitian

Hodge theory and complex algebraic geometry

Introduction. Part I. The Topology of Algebraic Varieties: 1. The Lefschetz theorem on hyperplane sections 2. Lefschetz pencils 3. Monodromy 4. The Leray spectral sequence Part II. Variations of

Analytic torsion and holomorphic determinant bundles I. Bott-Chern forms and analytic torsion

We attach secondary invariants to any acyclic complex of holomorphic Hermitian vector bundles on a complex manifold. These were first introduced by Bott and Chern [Bot C]. Our new definition uses

The $K$-energy on hypersurfaces and stability

The notion of stability for a polarized projective variety was introduced by D. Mumford for the study of the moduli problem of projective varieties. The stability has been verified by Mumford for

Cohomology of Vector Bundles and Syzygies

1. Introduction 2. Schur functions and Schur complexes 3. Grassmannians and flag varieties 4. Bott's theorem 5. The geometric technique 6. The determinantal varieties 7. Higher rank varieties 8. The

Kähler-Einstein metrics and the generalized Futaki invariant

In 1983, Futaki introduced his famous invariant. This invariant generalizes the obstruction of Kazdan-Warner to prescribing Gauss curvature on S 2 (cf. [Ful l ) . The Futaki invariant is defined for

Kähler-Einstein metrics with positive scalar curvature

Abstract. In this paper, we prove that the existence of Kähler-Einstein metrics implies the stability of the underlying Kähler manifold in a suitable sense. In particular, this disproves a

Hyperdiscriminant polytopes, Chow polytopes, and Mabuchi energy asymptotics

Let X be a smooth, linearly normal algebraic variety. It is shown that the Mabuchi energy of X restricted to the Bergman metrics is completely determined by the X-hyperdiscriminant of format (n-1)

Discriminants, Resultants, and Multidimensional Determinants

Preface.- Introduction.- General Discriminants and Resultants.- Projective Dual Varieties and General Discriminants.- The Cayley Method of Studying Discriminants.- Associated Varieties and General

GEOMETRIC INVARIANT THEORY

HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and