Zobrazeno 1 - 10
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pro vyhledávání: '"de Borbon, Martin"'
Autor:
de Borbon, Martin, Panov, Dmitri
Let $\mathcal{H}$ be a hyperplane arrangement in $\mathbb{CP}^n$. We define a quadratic form $Q$ on $\mathbb{R}^{\mathcal{H}}$ that is entirely determined by the intersection poset of $\mathcal{H}$. Using the Bogomolov-Gieseker inequality for parabol
Externí odkaz:
http://arxiv.org/abs/2411.09573
Autor:
de Borbon, Martin, Spotti, Cristiano
We investigate aspects of the metric bubble tree for non-collapsing degenerations of (log) K\"ahler-Einstein metrics in complex dimensions one and two, and further describe a conjectural higher dimensional picture.
Externí odkaz:
http://arxiv.org/abs/2309.03705
Autor:
de Borbon, Martin, Panov, Dmitri
We show that general Dunkl connections on $\mathbb{C}^2$ do not preserve non-zero Hermitian forms. Our proof relies on recent understanding of the non-trivial topology of the moduli space of spherical tori with one conical point.
Comment: 37 pag
Comment: 37 pag
Externí odkaz:
http://arxiv.org/abs/2209.05958
Autor:
de Borbon, Martin, Panov, Dmitri
We use the Kobayashi-Hitchin correspondence for parabolic bundles to reprove the results of Troyanov and Luo-Tian regarding existence and uniqueness of conformal spherical metrics on the Riemann sphere with prescribed cone angles in the interval $(0,
Externí odkaz:
http://arxiv.org/abs/2109.10250
Autor:
de Borbon, Martin, Panov, Dmitri
Let $X$ be a complex manifold and let $g$ be a polyhedral metric on it inducing its topology. We say that $g$ is a polyhedral K\"ahler (PK) metric on $X$ if it is K\"ahler outside its singular set. The local geometry of PK metrics is modelled on PK c
Externí odkaz:
http://arxiv.org/abs/2106.13224
Autor:
de Borbon, Martin, Edwards, Gregory
We produce local Calabi-Yau metrics on $\mathbf C^2$ with conical singularities along three or more complex lines through the origin whose cone angles strictly violate the Troyanov condition. The tangent cone at the origin is a flat polyhedral K\"ahl
Externí odkaz:
http://arxiv.org/abs/2006.06065
Autor:
de Borbon, Martin, Legendre, Eveline
We show that any toric K\"ahler cone with smooth compact cross-section admits a family of Calabi-Yau cone metrics with conical singularities along its toric divisors. The family is parametrized by the Reeb cone and the angles are given explicitly in
Externí odkaz:
http://arxiv.org/abs/2005.03502
Autor:
de Borbon, Martin, Edwards, Gregory
Publikováno v:
Comment. Math. Helv. 96 (2021), 113-148
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 Schauder estimate of Guo-Song. We characterize the space of homogeneous
Externí odkaz:
http://arxiv.org/abs/2002.07668
Autor:
de Borbon, Martin, Spotti, Cristiano
We construct ALE Calabi-Yau metrics with cone singularities along the exceptional set of resolutions of $\mathbb{C}^n / \Gamma$ with non-positive discrepancies. In particular, this includes the case of the minimal resolution of two dimensional quotie
Externí odkaz:
http://arxiv.org/abs/1811.12773
Autor:
de Borbon, Martin, Spotti, Cristiano
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 K\"ahler-Einstein metrics of negative Ricci with a cuspidal point. As an application, we describe sin
Externí odkaz:
http://arxiv.org/abs/1804.06815