collaborators

6 papers

math.DG2026

Euclidean -systems and real PK arrangements

Martin de Borbon, Dmitri Panov, Alexander P. Veselov

We establish a correspondence between two structures arising in the geometry of hyperplane arrangements: Euclidean -systems and real polyhedral Kähler (PK) arrangements. We p…

math.DG2026

SNC Kähler-Einstein metrics and RCD spaces

Martin de Borbon, Cristiano Spotti

We show that Kähler-Einstein metrics with cone singularities along simple normal crossing (SNC) divisors define RCD spaces, both in the compact setting and in certain non-compact…

math.DG2026

The Hirzebruch quadratic form of a hyperplane arrangement and flat logarithmic connections

Martin de Borbon, Dmitri Panov

We prove that the Hirzebruch quadratic form of a complex hyperplane arrangement is non-positive on the set of stable weights, and we identify the zero locus within this set with fl…

math.AG2026

A Miyaoka-Yau inequality for hyperplane arrangements in

Martin de Borbon, Dmitri Panov

Let be a hyperplane arrangement in . We define a quadratic form on that is entirely determined by the intersection poset…

math.DG2026

Polyhedral Kähler metrics on

Martin de Borbon, Dmitri Panov

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

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.