Martin de Borbon | Publications

All my papers are available on arXiv

2026

arXiv

Euclidean \(\vee\)-systems and real PK arrangements

with Dmitri Panov and Alexander P. Veselov

arXiv:2607.04859

Bib HTML

@article{deBorbonPanovVeselov2026VSystems,
  author = {de Borbon, Martin and Panov, Dmitri and Veselov, Alexander P.},
  title = {Euclidean \(\vee\)-systems and real {PK} arrangements},
  journal = {arXiv:2607.04859},
  year = {2026},
  eprint = {2607.04859},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2607.04859}
}

BLMS

Simple normal crossing Kähler–Einstein metrics and RCD spaces

with Cristiano Spotti

Bulletin of the London Mathematical Society

Bib HTML

@article{deBorbonSpotti2026RCD,
  author = {de Borbon, Martin and Spotti, Cristiano},
  title = {Simple normal crossing {Kähler--Einstein} metrics and {RCD} spaces},
  journal = {Bulletin of the London Mathematical Society},
  year = {2026},
  volume = {58},
  number = {7},
  pages = {e70443},
  doi = {10.1112/blms.70443},
  url = {https://doi.org/10.1112/blms.70443}
}

arXiv

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

with Dmitri Panov

arXiv:2601.15430

Bib HTML

@article{deBorbonPanov2026HirzebruchQuadraticForm,
  author = {de Borbon, Martin and Panov, Dmitri},
  title = {The {Hirzebruch} quadratic form of a hyperplane arrangement and flat logarithmic connections},
  journal = {arXiv:2601.15430},
  year = {2026},
  eprint = {2601.15430},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2601.15430}
}

JLMS

A Miyaoka–Yau inequality for hyperplane arrangements in \(\mathbb{CP}^n\)

with Dmitri Panov

Journal of the London Mathematical Society

Bib HTML

@article{deBorbonPanov2026MiyaokaYau,
  author = {de Borbon, Martin and Panov, Dmitri},
  title = {A {Miyaoka--Yau} inequality for hyperplane arrangements in \(\mathbb{CP}^n\)},
  journal = {Journal of the London Mathematical Society},
  year = {2026},
  volume = {113},
  number = {4},
  pages = {e70525},
  doi = {10.1112/jlms.70525},
  url = {https://doi.org/10.1112/jlms.70525}
}

2025

arXiv

Polyhedral Kähler metrics on \(\mathbb{CP}^n\)

with Dmitri Panov

arXiv:2510.17447

Bib HTML

@article{deBorbonPanov2025PolyhedralKahler,
  author = {de Borbon, Martin and Panov, Dmitri},
  title = {Polyhedral {Kähler} metrics on \(\mathbb{CP}^n\)},
  journal = {arXiv:2510.17447},
  year = {2025},
  eprint = {2510.17447},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2510.17447}
}

QJM

Local classification of Kähler metrics with constant holomorphic sectional curvature

The Quarterly Journal of Mathematics

Bib HTML

@article{deBorbon2025HolomorphicCurvature,
  author = {de Borbon, Martin},
  title = {Local classification of {Kähler} metrics with constant holomorphic sectional curvature},
  journal = {The Quarterly Journal of Mathematics},
  year = {2025},
  pages = {haaf046},
  doi = {10.1093/qmath/haaf046},
  url = {https://doi.org/10.1093/qmath/haaf046}
}

2024

AUF

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

with Cristiano Spotti

Annali dell'Università di Ferrara

Bib HTML

@article{deBorbonSpotti2024Bubbling,
  author = {de Borbon, Martin and Spotti, Cristiano},
  title = {Some models for bubbling of (log) {Kähler--Einstein} metrics},
  journal = {Annali dell'Università di Ferrara},
  year = {2024},
  volume = {70},
  pages = {1037--1068},
  doi = {10.1007/s11565-024-00520-w},
  url = {https://doi.org/10.1007/s11565-024-00520-w}
}

AFST

Dunkl connections on \(\mathbb{C}^2\) and spherical metrics

with Dmitri Panov

Annales de la Faculté des Sciences de Toulouse

Bib HTML

@article{deBorbonPanov2024DunklConnections,
  author = {de Borbon, Martin and Panov, Dmitri},
  title = {Dunkl connections on \(\mathbb{C}^2\) and spherical metrics},
  journal = {Annales de la Faculté des Sciences de Toulouse},
  year = {2024},
  volume = {33},
  number = {4},
  pages = {937--979},
  doi = {10.5802/afst.1791},
  url = {https://doi.org/10.5802/afst.1791}
}

2023

JDG

Calabi–Yau metrics with conical singularities along line arrangements

with Cristiano Spotti

Journal of Differential Geometry

Bib HTML

@article{deBorbonSpotti2023LineArrangements,
  author = {de Borbon, Martin and Spotti, Cristiano},
  title = {Calabi--Yau metrics with conical singularities along line arrangements},
  journal = {Journal of Differential Geometry},
  year = {2023},
  doi = {10.4310/jdg/1680883576},
  url = {https://doi.org/10.4310/jdg/1680883576}
}

2022

JLMS

Calabi–Yau metrics with cone singularities along intersecting complex lines: The unstable case

with Gregory Edwards

Journal of the London Mathematical Society

Bib HTML

@article{deBorbonEdwards2022UnstableCase,
  author = {de Borbon, Martin and Edwards, Gregory},
  title = {Calabi--Yau metrics with cone singularities along intersecting complex lines: The unstable case},
  journal = {Journal of the London Mathematical Society},
  year = {2022},
  doi = {10.1112/jlms.12558},
  url = {https://doi.org/10.1112/jlms.12558}
}

Selecta

Toric Sasaki–Einstein metrics with conical singularities

with Eveline Legendre

Selecta Mathematica

Bib HTML

@article{deBorbonLegendre2022ToricSasakiEinstein,
  author = {de Borbon, Martin and Legendre, Eveline},
  title = {Toric {Sasaki--Einstein} metrics with conical singularities},
  journal = {Selecta Mathematica},
  year = {2022},
  doi = {10.1007/s00029-022-00778-y},
  url = {https://doi.org/10.1007/s00029-022-00778-y}
}

Proc. AMS

Parabolic bundles and spherical metrics

with Dmitri Panov

Proceedings of the American Mathematical Society

Bib HTML

@article{deBorbonPanov2022ParabolicBundles,
  author = {de Borbon, Martin and Panov, Dmitri},
  title = {Parabolic bundles and spherical metrics},
  journal = {Proceedings of the American Mathematical Society},
  year = {2022},
  doi = {10.1090/proc/16052},
  url = {https://doi.org/10.1090/proc/16052}
}

2021

CMH

Schauder estimates on products of cones

with Gregory Edwards

Commentarii Mathematici Helvetici

Bib HTML

@article{deBorbonEdwards2021Schauder,
  author = {de Borbon, Martin and Edwards, Gregory},
  title = {Schauder estimates on products of cones},
  journal = {Commentarii Mathematici Helvetici},
  year = {2021},
  volume = {96},
  number = {1},
  pages = {113--148},
  doi = {10.4171/cmh/509},
  url = {https://doi.org/10.4171/cmh/509}
}

arXiv

Polyhedral Kähler cone metrics on \(\mathbb{C}^n\) singular at hyperplane arrangements

with Dmitri Panov

arXiv:2106.13224

Bib HTML

@article{deBorbonPanov2021PolyhedralKahler,
  author = {de Borbon, Martin and Panov, Dmitri},
  title = {Polyhedral {Kähler} cone metrics on \(\mathbb{C}^n\) singular at hyperplane arrangements},
  journal = {arXiv:2106.13224},
  year = {2021},
  eprint = {2106.13224},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2106.13224}
}

2019

IMRN

Asymptotically conical Calabi–Yau metrics with cone singularities along a compact divisor

with Cristiano Spotti

International Mathematics Research Notices

Bib HTML

@article{deBorbonSpotti2019AsymptoticallyConical,
  author = {de Borbon, Martin and Spotti, Cristiano},
  title = {Asymptotically conical {Calabi--Yau} metrics with cone singularities along a compact divisor},
  journal = {International Mathematics Research Notices},
  year = {2019},
  number = {2},
  pages = {1198--1223},
  doi = {10.1093/imrn/rnz280},
  url = {https://doi.org/10.1093/imrn/rnz280}
}

Proc. AMS

Local models for conical Kähler–Einstein metrics

with Cristiano Spotti

Proceedings of the American Mathematical Society

Bib HTML

@article{deBorbonSpotti2019LocalModels,
  author = {de Borbon, Martin and Spotti, Cristiano},
  title = {Local models for conical {Kähler--Einstein} metrics},
  journal = {Proceedings of the American Mathematical Society},
  year = {2019},
  volume = {147},
  number = {3},
  pages = {1217--1230},
  doi = {10.1090/proc/14302},
  url = {https://doi.org/10.1090/proc/14302}
}

2017

AGAG

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

Annals of Global Analysis and Geometry

Bib HTML

@article{deBorbon2017BoundedRicci,
  author = {de Borbon, Martin},
  title = {Kähler metrics with cone singularities along a divisor of bounded {Ricci} curvature},
  journal = {Annals of Global Analysis and Geometry},
  year = {2017},
  volume = {52},
  number = {4},
  pages = {457--464},
  doi = {10.1007/s10455-017-9565-1},
  url = {https://doi.org/10.1007/s10455-017-9565-1}
}

JGP

The Gibbons–Hawking ansatz over a wedge

Journal of Geometry and Physics

Bib HTML

@article{deBorbon2017GibbonsHawking,
  author = {de Borbon, Martin},
  title = {The {Gibbons--Hawking} ansatz over a wedge},
  journal = {Journal of Geometry and Physics},
  year = {2017},
  volume = {120},
  pages = {228--241},
  doi = {10.1016/j.geomphys.2017.06.002},
  url = {https://doi.org/10.1016/j.geomphys.2017.06.002}
}

JLMS

Asymptotically conical Ricci-flat Kähler metrics on \(\mathbb{C}^2\) with cone singularities along a complex curve

Journal of the London Mathematical Society

Bib HTML

@article{deBorbon2017ACRicciFlat,
  author = {de Borbon, Martin},
  title = {Asymptotically conical {Ricci}-flat {Kähler} metrics on \(\mathbb{C}^2\) with cone singularities along a complex curve},
  journal = {Journal of the London Mathematical Society},
  year = {2017},
  volume = {96},
  number = {2},
  pages = {425--454},
  doi = {10.1112/jlms.12070},
  url = {https://doi.org/10.1112/jlms.12070}
}

COMA

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

Complex Manifolds

Bib HTML

@article{deBorbon2017TangentCones,
  author = {de Borbon, Martin},
  title = {Singularities of plane complex curves and limits of {Kähler} metrics with cone singularities. {I}: Tangent cones},
  journal = {Complex Manifolds},
  year = {2017},
  volume = {4},
  number = {1},
  pages = {43--72},
  doi = {10.1515/coma-2017-0005},
  url = {https://doi.org/10.1515/coma-2017-0005}
}