Publications

2025

1. arXiv

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

   dB, M., and Panov, Dmitri

   arXiv 2025

   Bib HTML

   @article{cpn,
     abbr = {arXiv},
     bibtex_show = {false},
     html = {https://arxiv.org/abs/2510.17447},
     title = {Polyhedral Kähler metrics on \(\mathbb{CP}^n\)},
     author = {dB, M. and Panov, Dmitri},
     journal = {arXiv},
     year = {2025}
   }

2. QJM

   Local classification of Kähler metrics with constant holomorphic sectional curvature

   dB, M.

   The Quarterly Journal of Mathematics 2025

   Abs Bib HTML

   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.

   @article{chsc,
     abbr = {QJM},
     bibtex_show = {false},
     html = {https://doi.org/10.1093/qmath/haaf046},
     author = {dB, M.},
     title = {Local classification of Kähler metrics with constant holomorphic sectional curvature},
     journal = {The Quarterly Journal of Mathematics},
     pages = {haaf046},
     year = {2025},
     issn = {0033-5606},
     doi = {10.1093/qmath/haaf046},
     url = {https://doi.org/10.1093/qmath/haaf046},
     eprint = {https://academic.oup.com/qjmath/advance-article-pdf/doi/10.1093/qmath/haaf046/65669322/haaf046.pdf}
   }

2024

1. arXiv

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

   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}
   }

2. 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}
   }

3. AFST

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

   dB, M., and Panov, Dmitri

   Annales de la Facultè des Sciences de Toulouse 2024

   Bib HTML

   @article{dunkl,
     abbr = {AFST},
     bibtex_show = {false},
     html = {https://afst.centre-mersenne.org/articles/10.5802/afst.1791/},
     title = {Dunkl connections on  \(\mathbb{C}^2\) and spherical metrics},
     author = {dB, M. and Panov, Dmitri},
     journal = {Annales de la Facultè des Sciences de Toulouse},
     pages = {937--979},
     year = {2024},
     publisher = {Universit\'e Paul Sabatier, Toulouse},
     volume = {Ser. 6, 33},
     number = {4},
     doi = {10.5802/afst.1791},
     language = {en},
     url = {https://afst.centre-mersenne.org/articles/10.5802/afst.1791/}
   }

2023

1. 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

1. 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}
   }

2. 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}
   }

3. 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

1. 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}
   }

2. arXiv

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

1. 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}
   }

2. 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

1. 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}
   }

2. 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}
   }

3. JLMS

   Asymptotically conical Ricci-flat Kähler metrics on \(\mathbb{C}^2\) 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}
   }

4. 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}
   }