Martin de Borbon | Publications

All my papers are available on arXiv

2024

arXiv

A Miyaoka-Yau inequality for hyperplane arrangements in

{CP}^{n}

dB, M., and Panov, Dmitri

arXiv 2024

Bib HTML

@article{miyaokayau,
  abbr = {arXiv},
  bibtex_show = {false},
  html = {https://arxiv.org/abs/2411.09573},
  title = {A Miyaoka-Yau inequality for hyperplane arrangements in \(\mathbb{CP}^n\)},
  author = {dB, M. and Panov, Dmitri},
  journal = {arXiv},
  year = {2024}
}

AUF

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

dB, M., and Spotti, Cristiano

Ann. Univ. Ferrara 2024

Bib HTML

@article{bubbles,
  abbr = {AUF},
  bibtex_show = {false},
  html = {https://link.springer.com/article/10.1007/s11565-024-00520-w},
  title = {Some models for bubbling of (log) Kähler-Einstein metrics},
  author = {dB, M. and Spotti, Cristiano},
  journal = {Ann. Univ. Ferrara},
  volume = {70},
  pages = {1037--1068},
  year = {2024}
}

2023

JDG

Calabi-Yau metrics with conical singularities along line arrangements

dB, M., and Spotti, Cristiano

Journal of Differential Geometry 2023

Bib HTML

@article{linearrangements,
  abbr = {JDG},
  bibtex_show = {false},
  html = {https://projecteuclid.org/journals/journal-of-differential-geometry/volume-123/issue-2/CalabiYau-metrics-with-conical-singularities-along-line-arrangements/10.4310/jdg/1680883576.short},
  title = {Calabi-Yau metrics with conical singularities along line arrangements},
  author = {dB, M. and Spotti, Cristiano},
  journal = {Journal of Differential Geometry},
  year = {2023}
}

2022

AFST

Dunkl connections on

C^{2}

and spherical metrics

dB, M., and Panov, Dmitri

to appear in Ann. Fac. Sci. Toulouse 2022

Bib HTML

@article{dunkl,
  abbr = {AFST},
  bibtex_show = {false},
  html = {https://arxiv.org/abs/2209.05958},
  title = {Dunkl connections on  \(\mathbb{C}^2\) and spherical metrics},
  author = {dB, M. and Panov, Dmitri},
  journal = {to appear in Ann. Fac. Sci. Toulouse},
  year = {2022}
}

JLMS

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

dB, M., and Edwards, Gregory

J. Lond. Math. Soc. 2022

Bib HTML

@article{3lines,
  abbr = {JLMS},
  bibtex_show = {false},
  html = {https://londmathsoc.onlinelibrary.wiley.com/doi/abs/10.1112/jlms.12558},
  author = {dB, M. and Edwards, Gregory},
  title = {Calabi-Yau metrics with cone singularities along intersecting complex lines: the unstable case},
  journal = {J. Lond. Math. Soc.},
  fjournal = {Journal of the London Mathematical Society.},
  volume = {},
  year = {2022},
  number = {},
  pages = {},
  issn = {},
  mrclass = {},
  mrnumber = {},
  mrreviewer = {},
  doi = {10.1112/jlms.12558},
  url = {https://doi.org/10.1112/jlms.12558}
}

Selecta

Toric Sasaki-Einstein metrics with conical singularities

dB, M., and Legendre, Eveline

Selecta Mathematica 2022

Bib HTML

@article{toric,
  abbr = {Selecta},
  bibtex_show = {false},
  html = {https://link.springer.com/article/10.1007/s00029-022-00778-y},
  title = {Toric Sasaki-Einstein metrics with conical singularities},
  author = {dB, M. and Legendre, Eveline},
  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

dB, M., and Panov, Dmitri

Proc. Amer. Math. Soc. 2022

Bib HTML

@article{parabolic,
  abbr = {Proc. AMS},
  bibtex_show = {false},
  html = {https://doi.org/10.1090/proc/16052},
  title = {Parabolic bundles and spherical metrics},
  author = {dB, M. and Panov, Dmitri},
  journal = {Proc. Amer. Math. Soc.},
  year = {2022},
  doi = {https://doi.org/10.1090/proc/16052}
}

2021

CMH

Schauder estimates on products of cones

dB, M., and Edwards, Gregory

Comment. Math. Helv. 2021

Bib HTML

@article{schauder,
  abbr = {CMH},
  bibtex_show = {false},
  html = {https://www.ems-ph.org/journals/show_abstract.php?issn=0010-2571&vol=96&iss=1&rank=5&p403=1},
  author = {dB, M. and Edwards, Gregory},
  title = {Schauder estimates on products of cones},
  journal = {Comment. Math. Helv.},
  fjournal = {Commentarii Mathematici Helvetici. A Journal of the Swiss
                Mathematical Society},
  volume = {96},
  year = {2021},
  number = {1},
  pages = {113--148},
  issn = {0010-2571},
  mrclass = {35J75 (32Q15 35R01)},
  mrnumber = {4228616},
  doi = {10.4171/cmh/509},
  url = {https://doi.org/10.4171/cmh/509}
}

arXiv

Polyhedral Kähler cone metrics on

C^{n}

singular at hyperplane arrangements

dB, M., and Panov, Dmitri

arXiv 2021

Bib HTML

@article{pk,
  abbr = {arXiv},
  bibtex_show = {false},
  html = {https://arxiv.org/abs/2106.13224},
  title = {Polyhedral Kähler cone metrics on  \(\mathbb{C}^n\) singular at hyperplane arrangements},
  author = {dB, M. and Panov, Dmitri},
  journal = {arXiv},
  year = {2021}
}

2019

IMRN

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

dB, M., and Spotti, Cristiano

Int. Math. Res. Not. 2019

Bib HTML

@article{ale,
  abbr = {IMRN},
  bibtex_show = {false},
  html = {https://academic.oup.com/imrn/article-abstract/2021/2/1198/5640301},
  author = {dB, M. and Spotti, Cristiano},
  title = {Asymptotically conical Calabi-Yau metrics with cone
  	singularities along a compact divisor},
  journal = {Int. Math. Res. Not.},
  fjournal = {International Mathematics Research Notices. IMRN},
  year = {2019},
  number = {2},
  pages = {1198--1223},
  issn = {1073-7928},
  mrclass = {32Q25 (14J32 32M10 53C55)},
  mrnumber = {4201965},
  doi = {10.1093/imrn/rnz280},
  url = {https://doi.org/10.1093/imrn/rnz280}
}

Proc. AMS

Local models for conical Kähler-Einstein metrics

dB, M., and Spotti, Cristiano

Proc. Amer. Math. Soc. 2019

Bib HTML

@article{localmodels,
  abbr = {Proc. AMS},
  bibtex_show = {false},
  html = {https://www.ams.org/journals/proc/2019-147-03/S0002-9939-2018-14302-6/},
  author = {dB, M. and Spotti, Cristiano},
  title = {Local models for conical Kähler-Einstein metrics},
  journal = {Proc. Amer. Math. Soc.},
  fjournal = {Proceedings of the American Mathematical Society},
  volume = {147},
  year = {2019},
  number = {3},
  pages = {1217--1230},
  issn = {0002-9939},
  mrclass = {53C55 (53C25)},
  mrnumber = {3896068},
  mrreviewer = {Chengjian Yao},
  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

dB, M.

Ann. Global Anal. Geom. 2017

Bib HTML

@article{boundedricci,
  abbr = {AGAG},
  bibtex_show = {false},
  html = {https://link.springer.com/article/10.1007/s10455-017-9565-1},
  author = {dB, M.},
  title = {Kähler metrics with cone singularities along a divisor of
  	bounded Ricci curvature},
  journal = {Ann. Global Anal. Geom.},
  fjournal = {Annals of Global Analysis and Geometry},
  volume = {52},
  year = {2017},
  number = {4},
  pages = {457--464},
  issn = {0232-704X},
  mrclass = {32Q15 (53C55)},
  mrnumber = {3735907},
  mrreviewer = {Rafa\l  Czy\.{z}},
  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

dB, M.

J. Geom. Phys. 2017

Bib HTML

@article{gibbonshawking,
  abbr = {JGP},
  bibtex_show = {false},
  html = {https://www.sciencedirect.com/science/article/pii/S0393044017301584?via%3Dihub},
  author = {dB, M.},
  title = {The Gibbons-Hawking ansatz over a wedge},
  journal = {J. Geom. Phys.},
  fjournal = {Journal of Geometry and Physics},
  volume = {120},
  year = {2017},
  pages = {228--241},
  issn = {0393-0440},
  mrclass = {53C55 (31C12 32Q15 32Q26 53C21)},
  mrnumber = {3712159},
  mrreviewer = {Bogdan D. Suceav\u{a}},
  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

C^{2}

with cone singularities along a complex curve

dB, M.

J. Lond. Math. Soc. 2017

Bib HTML

@article{acrf,
  abbr = {JLMS},
  bibtex_show = {false},
  html = {https://londmathsoc.onlinelibrary.wiley.com/doi/abs/10.1112/jlms.12070},
  author = {dB, M.},
  title = {Asymptotically conical Ricci-flat Kähler metrics on \(\mathbb{C}^2\) with cone singularities along a complex curve},
  journal = {J. Lond. Math. Soc.},
  fjournal = {Journal of the London Mathematical Society. Second Series},
  volume = {96},
  year = {2017},
  number = {2},
  pages = {425--454},
  issn = {0024-6107},
  mrclass = {53C55 (14J32 32W20 53C21 53C25 58J05)},
  mrnumber = {3708957},
  mrreviewer = {Ronan J. Conlon},
  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

dB, M.

Complex Manifolds 2017

Bib HTML

@article{tangentcones,
  abbr = {COMA},
  bibtex_show = {false},
  html = {https://www.degruyter.com/document/doi/10.1515/coma-2017-0005/html},
  author = {dB, M.},
  title = {Singularities of plane complex curves and limits of Kähler
  	metrics with cone singularities. I: Tangent cones},
  journal = {Complex Manifolds},
  fjournal = {Complex Manifolds},
  volume = {4},
  year = {2017},
  number = {1},
  pages = {43--72},
  mrclass = {53C55 (32Q20 53C25)},
  mrnumber = {3627149},
  mrreviewer = {Antonella Nannicini},
  doi = {10.1515/coma-2017-0005},
  url = {https://doi.org/10.1515/coma-2017-0005}
}