Martin de Borbon

activity

20152026

most citedSingularities of plane complex curves and limits of Kähler metrics with cone singularities. I: Tangent Cones

4 citations · 21 across the 16 of their papers we have counts for

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17 papers · 1 filter

math.DG2026

Point-balanced arrangements in the real projective plane and the Hirzebruch property

Martin de Borbon

A collection of $m \geq 2$ lines through the origin in $R^{2}$ is balanced if the sum of the orthogonal projections onto these lines equals $m /2$ times the identity. A line…

math.DG2026

Kähler-Einstein cone metrics and parabolic bundles

Martin de Borbon

Let $X$ be a compact Kähler manifold, let $D = \sum_{i} D_{i}$ be a simple normal crossing divisor, and fix $β_{i} \in (0, 1)$ . We introduce a parabolic structure $T X_{*}$ on $T X$ , given along e…

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…

math.DG2023

Some models for bubbling of (log) Kähler-Einstein metrics

Martin de Borbon, Cristiano Spotti

We investigate aspects of the metric bubble tree for non-collapsing degenerations of (log) Kähler-Einstein metrics in complex dimensions one and two, and further describe a conject…

math.DG2020

Calabi-Yau metrics with cone singularities along intersecting complex lines: the unstable case

Martin de Borbon, Gregory Edwards

We produce local Calabi-Yau metrics on $C^{2}$ with conical singularities along three or more complex lines through the origin whose cone angles strictly violate the Troyanov…

math.DG2020★ 4 cited

Schauder estimates on products of cones

Martin de Borbon, Gregory Edwards

We prove an interior Schauder estimate for the Laplacian on metric products of two dimensional cones with a Euclidean factor, generalizing the work of Donaldson and reproving the S…

math.DG2018★ 3 cited

ALE Calabi-Yau metrics with conical singularities along a compact divisor

Martin de Borbon, Cristiano Spotti

We construct ALE Calabi-Yau metrics with cone singularities along the exceptional set of resolutions of $C^{n} /Γ$ with non-positive discrepancies. In particular, this incl…

math.DG2018★ 3 cited

Local models for conical Kähler-Einstein metrics

Martin de Borbon, Cristiano Spotti

In this note we use the Calabi ansatz, in the context of metrics with conical singularities along a divisor, to produce regular Calabi-Yau cones and Kähler-Einstein metrics of nega…

math.DG2017★ 3 cited

Calabi-Yau metrics with conical singularities along line arrangements

Martin de Borbon, Cristiano Spotti

Given a weighted line arrangement in the projective plane, with weights satisfying natural constraint conditions, we show the existence of a Ricci-flat Kähler metric with cone sing…

math.DG2017★ 2 cited

The Gibbons-Hawking ansatz over a wedge

Martin de Borbon

We discuss the Ricci-flat `model metrics' on $C^{2}$ with cone singularities along the conic ${z w = 1}$ constructed by Donaldson using the Gibbons-Hawking ansatz over wedges…

math.DG2016★ 2 cited

Kähler metrics with cone singularities along a divisor of bounded Ricci curvature

Martin de Borbon

Let $D$ be a smooth divisor in a compact complex manifold $X$ and let $β \in (0, 1)$ . We show that in any positive co-homology class on $X$ there is a Kähler metric with cone angle $…

math.DG2016★ 4 cited

Singularities of plane complex curves and limits of Kähler metrics with cone singularities. I: Tangent Cones

Martin de Borbon

We construct and classify, in the case of two complex dimensions, the possible tangent cones at points of limit spaces of non-collapsed sequences of Kähler-Einstein metrics with co…

math.DG2015

Asymptotically conical Ricci flat Kähler metrics on $C^{2}$ with cone singularities along a complex curve

Martin de Borbon

We prove an existence theorem for Asymptotically Conical Ricci Flat Kahler metrics in $C^{2}$ with cone singularities along a smooth complex curve. These metrics are expecte…

Point-balanced arrangements in the real projective plane and the Hirzebruch property

Kähler-Einstein cone metrics and parabolic bundles

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

Some models for bubbling of (log) Kähler-Einstein metrics

Calabi-Yau metrics with cone singularities along intersecting complex lines: the unstable case

Schauder estimates on products of cones

ALE Calabi-Yau metrics with conical singularities along a compact divisor

Local models for conical Kähler-Einstein metrics

Calabi-Yau metrics with conical singularities along line arrangements

The Gibbons-Hawking ansatz over a wedge

Kähler metrics with cone singularities along a divisor of bounded Ricci curvature

Singularities of plane complex curves and limits of Kähler metrics with cone singularities. I: Tangent Cones

Asymptotically conical Ricci flat Kähler metrics on C2 with cone singularities along a complex curve

Euclidean $\lor$ -systems and real PK arrangements

Asymptotically conical Ricci flat Kähler metrics on $C^{2}$ with cone singularities along a complex curve