Results 21 to 30 of about 305 (88)
Canonical complex extensions of Kähler manifolds
Journal of the London Mathematical Society, Volume 101, Issue 2, Page 786-827, April 2020., 2020 Abstract Given a complex manifold X, any Kähler class defines an affine bundle over X, and any Kähler form in the given class defines a totally real embedding of X into this affine bundle. We formulate conditions under which the affine bundles arising this way are Stein and relate this question to other natural positivity conditions on the tangent ...
Daniel Greb, Michael Lennox Wong
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The symplectic density property for Calogero–Moser spaces
Journal of the London Mathematical Society, Volume 111, Issue 2, February 2025.Abstract We introduce the symplectic density property and the Hamiltonian density property together with the corresponding versions of Andersén–Lempert theory. We establish these properties for the Calogero–Moser space Cn$\mathcal {C}_n$ of n$n$ particles and describe its group of holomorphic symplectic automorphisms.
Rafael B. Andrist, Gaofeng Huang
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Curvature of quaternionic skew‐Hermitian manifolds and bundle constructions
Mathematische Nachrichten, Volume 298, Issue 1, Page 87-112, January 2025.Abstract This paper is devoted to a description of the second‐order differential geometry of torsion‐free almost quaternionic skew‐Hermitian manifolds, that is, of quaternionic skew‐Hermitian manifolds (M,Q,ω)$(M, Q, \omega)$. We provide a curvature characterization of such integrable geometric structures, based on the holonomy theory of symplectic ...
Ioannis Chrysikos +2 more
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Characteristic foliations — A survey
Bulletin of the London Mathematical Society, Volume 56, Issue 7, Page 2231-2249, July 2024.Abstract This is a survey article, with essentially complete proofs, of a series of recent results concerning the geometry of the characteristic foliation on smooth divisors in compact hyperkähler manifolds, starting with work by Hwang–Viehweg, but also covering articles by Amerik–Campana and Abugaliev.
Fabrizio Anella, Daniel Huybrechts
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Subquadratic harmonic functions on Calabi‐Yau manifolds with maximal volume growth
Communications on Pure and Applied Mathematics, Volume 77, Issue 6, Page 3080-3106, June 2024.Abstract On a complete Calabi‐Yau manifold M$M$ with maximal volume growth, a harmonic function with subquadratic polynomial growth is the real part of a holomorphic function. This generalizes a result of Conlon‐Hein. We prove this result by proving a Liouville‐type theorem for harmonic 1‐forms, which follows from a new local L2$L^2$ estimate of the ...
Shih‐Kai Chiu
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Gravitational instantons with quadratic volume growth
Journal of the London Mathematical Society, Volume 109, Issue 4, April 2024.Abstract There are two known classes of gravitational instantons with quadratic volume growth at infinity, known as type ALG$\operatorname{ALG}$ and ALG∗$\operatorname{ALG}^*$. Gravitational instantons of type ALG$\operatorname{ALG}$ were previously classified by Chen–Chen.
Gao Chen, Jeff Viaclovsky
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Closed 3‐forms in five dimensions and embedding problems
Journal of the London Mathematical Society, Volume 109, Issue 4, April 2024.Abstract We consider the question if a five‐dimensional manifold can be embedded into a Calabi–Yau manifold of complex dimension 3 such that the real part of the holomorphic volume form induces a given closed 3‐form on the 5‐manifold. We define an open set of 3‐forms in dimension five which we call strongly pseudoconvex, and show that for closed ...
Simon Donaldson, Fabian Lehmann
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Integrability of Einstein deformations and desingularizations
Communications on Pure and Applied Mathematics, Volume 77, Issue 1, Page 177-220, January 2024.Abstract We study the question of the integrability of Einstein deformations and relate it to the question of the desingularization of Einstein metrics. Our main application is a negative answer to the long‐standing question of whether or not every Einstein 4‐orbifold (which is an Einstein metric space in a synthetic sense) is limit of smooth Einstein ...
Tristan Ozuch
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One‐dimensional local families of complex K3 surfaces
Bulletin of the London Mathematical Society, Volume 56, Issue 1, Page 296-305, January 2024.Abstract For any complex K3 surface X$X$, we construct a one‐dimensional deformation in which all integers ρ$\rho$ with 0⩽ρ⩽20$0 \leqslant \rho \leqslant 20$ occur as Picard numbers of some fibres. In contrast, we prove that the generic one‐dimensional local family of K3 surfaces admits only 0 and 1 as Picard numbers of the fibres.
Riccardo Carini, Francesco Viganò
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Towards generic base-point-freeness for hyperkähler manifolds of generalized Kummer type [PDF]
, 2022 Mauro Varesco
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