4 citations · 21 across the 16 of their papers we have counts for
17 papers
Point-balanced arrangements in the real projective plane and the Hirzebruch property
Martin de Borbon
A collection of lines through the origin in is balanced if the sum of the orthogonal projections onto these lines equals times the identity. A line…
Kähler-Einstein cone metrics and parabolic bundles
Martin de Borbon
Let be a compact Kähler manifold, let be a simple normal crossing divisor, and fix . We introduce a parabolic structure on , given along e…
Local classification of chsc Kähler metrics with cone singularities
Martin de Borbon
Let be a ball centred at the origin and . Let be a Kähler metric of constant holomorphic sectional curvature (chsc) on , unifo…
Curvature growth and holomorphic splitting for Kähler metrics with cone singularities
Martin de Borbon
We study Kähler metrics with cone angle along a smooth divisor, in the range . We show that bounded Riemann curvature near the divisor forces the normal bundle seque…
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…
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…
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…
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…
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 with conical singularities along three or more complex lines through the origin whose cone angles strictly violate the Troyanov…
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…
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 with non-positive discrepancies. In particular, this incl…
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…
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…
The Gibbons-Hawking ansatz over a wedge
Martin de Borbon
We discuss the Ricci-flat `model metrics' on with cone singularities along the conic constructed by Donaldson using the Gibbons-Hawking ansatz over wedges…
Kähler metrics with cone singularities along a divisor of bounded Ricci curvature
Martin de Borbon
Let be a smooth divisor in a compact complex manifold and let . We show that in any positive co-homology class on there is a Kähler metric with cone angle $…
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…
Asymptotically conical Ricci flat Kähler metrics on with cone singularities along a complex curve
Martin de Borbon
We prove an existence theorem for Asymptotically Conical Ricci Flat Kahler metrics in with cone singularities along a smooth complex curve. These metrics are expecte…