6 papers
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…
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…
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…
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…
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.