Martin de Borbon

collaborators

5 papers

math.DG2026

Local classification of chsc Kähler metrics with cone singularities

Martin de Borbon

Let $B \subset C^{n}$ be a ball centred at the origin and $D = {z^{1} = 0}$ . Let $g$ be a Kähler metric of constant holomorphic sectional curvature (chsc) on $B ∖ D$ , unifo…

math.DG2026

Curvature growth and holomorphic splitting for Kähler metrics with cone singularities

Martin de Borbon

We study Kähler metrics with cone angle $2 π β$ along a smooth divisor, in the range $1/2 < β < 1$ . We show that bounded Riemann curvature near the divisor forces the normal bundle seque…

math.DG2026

Euclidean $\lor$ -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 $\lor$ -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 c…

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…

Local classification of chsc Kähler metrics with cone singularities

Curvature growth and holomorphic splitting for Kähler metrics with cone singularities

Euclidean ∨-systems and real PK arrangements

SNC Kähler-Einstein metrics and RCD spaces

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

Euclidean $\lor$ -systems and real PK arrangements