Martin de Borbon

activity

20212025

most citedPolyhedral Kähler cone metrics on

C^{n}

singular at hyperplane arrangements

2 citations · 2 across the 6 of their papers we have counts for

collaborators

6 papers

math.DG2025

Polyhedral Kähler metrics on $CP^{n}$

Martin de Borbon, Dmitri Panov

We give necessary and sufficient conditions for the existence of polyhedral Kähler metrics on $CP^{n}$ whose singular set is a hyperplane arrangement and whose cone angles a…

math.DG2025

Local classification of Kähler metrics with constant holomorphic sectional curvature

Martin de Borbon

We prove the local classification of Kähler metrics with constant holomorphic sectional curvature by exploiting the geometry of the bundle of 1-jets of holomorphic functions.

math.AG2024

A Miyaoka-Yau inequality for hyperplane arrangements in $CP^{n}$

Martin de Borbon, Dmitri Panov

Let $H$ be a hyperplane arrangement in $CP^{n}$ . We define a quadratic form $Q$ on $R^{H}$ that is entirely determined by the intersection poset…

math.DG2022

Dunkl connections on $C^{2}$ and spherical metrics

Martin de Borbon, Dmitri Panov

We show that general Dunkl connections on $C^{2}$ do not preserve non-zero Hermitian forms. Our proof relies on recent understanding of the non-trivial topology of the modul…

math.DG2021

Parabolic bundles and spherical metrics

Martin de Borbon, Dmitri Panov

We use the Kobayashi-Hitchin correspondence for parabolic bundles to reprove the results of Troyanov and Luo-Tian regarding existence and uniqueness of conformal spherical metrics…

math.DG2021★ 2 cited

Polyhedral Kähler cone metrics on $C^{n}$ singular at hyperplane arrangements

Martin de Borbon, Dmitri Panov

Let $X$ be a complex manifold and let $g$ be a polyhedral metric on it inducing its topology. We say that $g$ is a polyhedral Kähler (PK) metric on $X$ if it is Kähler outside its…

Polyhedral Kähler metrics on CPn

Local classification of Kähler metrics with constant holomorphic sectional curvature

A Miyaoka-Yau inequality for hyperplane arrangements in CPn

Dunkl connections on C2 and spherical metrics

Parabolic bundles and spherical metrics

Polyhedral Kähler cone metrics on Cn singular at hyperplane arrangements

Polyhedral Kähler metrics on $CP^{n}$

A Miyaoka-Yau inequality for hyperplane arrangements in $CP^{n}$

Dunkl connections on $C^{2}$ and spherical metrics

Polyhedral Kähler cone metrics on $C^{n}$ singular at hyperplane arrangements