6 citations · 25 across the 13 of their papers we have counts for
19 papers
-critical equations for holomorphic vector bundles on Kähler surfaces
Julien Keller, Carlo Scarpa
We prove that the existence of a -positive and -critical Hermitian metric on a rank 2 holomorphic vector bundle over a compact Kähler surface implies that the bundle is -s…
Quot-scheme limit of Fubini-Study metrics and its applications to balanced metrics
Yoshinori Hashimoto, Julien Keller
We present some results that complement our prequels [arXiv:1809.08425,arXiv:1907.05770] on holomorphic vector bundles. We apply the method of the Quot-scheme limit of Fubini-Study…
A variational approach to the Hermitian-Einstein metrics and the Quot-scheme limit of Fubini-Study metrics
Yoshinori Hashimoto, Julien Keller
This is a sequel of our paper [arXiv:1809.08425] on the Quot-scheme limit and variational properties of Donaldson's functional, which established its coercivity for slope stable ho…
Quot-scheme limit of Fubini-Study metrics and Donaldson's functional for vector bundles
Yoshinori Hashimoto, Julien Keller
For a holomorphic vector bundle over a polarised Kähler manifold, we establish a direct link between the slope stability of and the asymptotic behaviour of Donaldson's func…
About J-flow, J-balanced metrics, uniform J-stability and K-stability
Yoshinori Hashimoto, Julien Keller
From the work of Dervan-Keller, there exists a quantization of the critical equation for the J-flow. This leads to the notion of J-balanced metrics. We prove that the existence of…
Construction of constant scalar curvature Kähler cone metrics
Julien Keller, Kai Zheng
Over a compact Kähler manifold, we provide a Fredholm alternative result for the Lichnerowicz operator associated to a Kähler metric with conic singularities along a divisor. We de…
Relative K-polystability of projective bundles over a curve
Vestislav Apostolov, Julien Keller
Let be the projectivization of a holomorphic vector bundle over a compact complex curve . We characterize the existence of an extremal Kähler metric on the ruled mani…
On the lower bounds of the L^2-norm of the Hermitian scalar curvature
Julien Keller, Mehdi Lejmi
On a pre-quantized symplectic manifold, we show that the symplectic Futaki invariant, which is an obstruction to the existence of constant Hermitian scalar curvature almost-Kähler…
Quantization of Hitchin's equations for Higgs Bundles I
Mario Garcia-Fernandez, Julien Keller, Julius Ross
We provide an algebraic framework for quantization of Hermitian metrics that are solutions of the Hitchin equation for Higgs bundles over a projective manifold. Using Geometric Inv…
A finite dimensional approach to Donaldson's J-flow
Ruadhaí Dervan, Julien Keller
We define a quantisation of the J-flow over a projective complex manifold. As corollaries, we obtain new proofs of uniqueness of critical points of the J-flow and that these critic…
Quantization of the Laplacian operator on vector bundles I
Julien Keller, Julien Meyer, Reza Seyyedali
Let be a holomorphic Hermitian vector bundle over a polarized manifold. We provide a canonical quantization of the Laplacian operator acting on sections of the bundle of He…
Quantization of Donaldson's heat flow over projective manifolds
Julien Keller, Reza Seyyedali
Consider a holomorphic vector bundle over a projective manifold polarized by an ample line bundle . Fix large enough, the holomorphic sections pr…
About projectivisation of Mumford semistable bundles over a curve
Julien Keller
We study the existence of canonical Kähler metrics on the projectivisation of strictly Mumford semistable holomorphic vector bundles over a complex curve. We also provide an algebr…
A note on Chow stability of the Projectivisation of Gieseker Stable Bundles
Julien Keller, Julius Ross
We investigate Chow stability of projective bundles P(E) where E is a strictly Gieseker stable bundle over a base manifold that has constant scalar curvature. We show that, for sui…
Non trivial examples of coupled equations for Kähler metrics and Yang-Mills connections
Julien Keller, Christina W. Tønnesen-Friedman
We provide non trivial examples of solutions to the system of coupled equations introduced by M. García-Fernández for the uniformization problem of a triple where is…
About the Calabi problem: a finite dimensional approach
H. -D. Cao, Julien Keller
Let us consider a projective manifold and a volume form. We define the gradient flow associated to the problem of -balanced metrics in the quantum formalism, the Ω$-balacing…
Numerical Weil-Petersson metrics on moduli spaces of Calabi-Yau manifolds
Julien Keller, Sergio Lukic
We introduce a simple and very fast algorithm that computes Weil-Petersson metrics on moduli spaces of polarized Calabi-Yau manifolds. Also, by using Donaldson's quantization link…
Ricci iterations on Kahler classes
Julien Keller
In this paper we consider the dynamical system involved by the Ricci operator on the space of Kähler metrics. A. Nadel has defined an iteration scheme given by the Ricci operator f…
Vortex type equations and canonical metrics
Julien Keller
We introduce a notion of Gieseker stability for a filtered holomorphic vector bundle over a projective manifold. We relate it to an analytic condition in terms of hermitian met…