Results 41 to 50 of about 2,953 (146)
A decomposition theorem for $\mathbb{Q}$-Fano Kähler–Einstein varieties
Comptes Rendus. MathématiqueLet $X$ be a $\mathbb{Q}$-Fano variety admitting a Kähler–Einstein metric. We prove that up to a finite quasi-étale cover, $X$ splits isometrically as a product of Kähler–Einstein $\mathbb{Q}$-Fano varieties whose tangent sheaf is stable with respect to ...
Druel, Stéphane +2 more
doaj +1 more source
On uniqueness of solutions to complex Monge–Ampère mean field equations
Bulletin of the London Mathematical Society, Volume 57, Issue 10, Page 3163-3180, October 2025.Abstract We establish the uniqueness of solutions to complex Monge–Ampère mean field equations when (minus) the temperature parameter is small. In the local setting of bounded hyperconvex domains, our result partially confirms a conjecture by Berman and Berndtsson. Our approach also extends to the global context of compact complex manifolds.
Chinh H. Lu, Trong‐Thuc Phung
wiley +1 more source
Holomorphic field theories and higher algebra
Bulletin of the London Mathematical Society, Volume 57, Issue 10, Page 2903-2974, October 2025.Abstract Aimed at complex geometers and representation theorists, this survey explores higher dimensional analogs of the rich interplay between Riemann surfaces, Virasoro and Kac‐Moody Lie algebras, and conformal blocks. We introduce a panoply of examples from physics — field theories that are holomorphic in nature, such as holomorphic Chern‐Simons ...
Owen Gwilliam, Brian R. Williams
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Einstein–Kähler metrics on certain complex bundles
, 2000 We study a class of compact complex manifolds, with positive first Chern class, fibered over products of projective spaces. We prove that these bundles carry Einstein–Kähler metrics when the projective spaces of the basis have the same dimension.
Ben Abdesselem, Adnène +3 more
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Weighted extremal Kähler metrics and the Einstein–Maxwell geometry of projective bundles
, 2022 We study the existence of weighted extremal Kähler metrics in the sense of [4, 32] on the total space of an admissible projective bundle over a Hodge Kähler manifold of constant scalar curvature.
Tønnesen-Friedman, Christina W. +2 more
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MathematicsThe manifolds studied are almost contact complex Riemannian manifolds, known also as almost contact B-metric manifolds. They are equipped with a pair of pseudo-Riemannian metrics that are mutually associated to each other using an almost contact ...
Mancho Manev
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Continuity of HYM connections with respect to metric variations
Journal of the London Mathematical Society, Volume 112, Issue 1, July 2025.Abstract We investigate the set of (real Dolbeault classes of) balanced metrics Θ$\Theta$ on a balanced manifold X$X$ with respect to which a torsion‐free coherent sheaf E$\mathcal {E}$ on X$X$ is slope stable. We prove that the set of all such [Θ]∈Hn−1,n−1(X,R)$[\Theta] \in H^{n - 1,n - 1}(X,\mathbb {R})$ is an open convex cone locally defined by a ...
Rémi Delloque
wiley +1 more source
Quasi-potentials and Kähler–Einstein metrics on flag manifolds, II
, 2003 For a homogeneous space G/P, where P is a parabolic subgroup of a complex semisimple group G, an explicit Kähler–Einstein metric on it is constructed. The Einstein constant for the metric is 1.
Azad, Hassan, Biswas, Indranil
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MathematicsAlmost contact complex Riemannian manifolds, also known as almost contact B-metric manifolds, are equipped with a pair of pseudo-Riemannian metrics that are mutually associated with each other using the tensor structure. Here, we consider a special class
Mancho Manev
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Simply connected positive Sasakian 5‐manifolds
Journal of the London Mathematical Society, Volume 112, Issue 1, July 2025.Abstract We investigate closed simply connected 5‐manifolds capable of hosting positive Sasakian structures. We present a conjectural comprehensive list of such manifolds.
Dasol Jeong, Jihun Park, Joonyeong Won
wiley +1 more source