Results 21 to 30 of about 257,471 (64)

Hyperkähler metrics near Lagrangian submanifolds and symplectic groupoids [PDF]

Journal für die Reine und Angewandte Mathematik, 2020
The first part of this paper is a generalization of the Feix–Kaledin theorem on the existence of a hyperkähler metric on a neighborhood of the zero section of the cotangent bundle of a Kähler manifold.
Maxence Mayrand
semanticscholar   +1 more source

Special Joyce structures and hyperkähler metrics [PDF]

Letters in Mathematical Physics
Joyce structures were introduced by T. Bridgeland in the context of the space of stability conditions of a three-dimensional Calabi–Yau category and its associated Donaldson–Thomas invariants. In subsequent work, T. Bridgeland and I. Strachan showed that
Iván Tulli
semanticscholar   +1 more source

Compact Tori Associated to Hyperkähler Manifolds of Kummer Type [PDF]

International mathematics research notices, 2018
Dedicato alla piccola Mia. For $X$ a hyperkähler manifold of Kummer type, let $J^3(X)$ be the intermediate Jacobian associated to $H^3(X)$. We prove that $H^2(X)$ can be embedded into $H^2(J^3(X))$.
K. O’Grady
semanticscholar   +1 more source

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
wiley   +1 more source

On the Hodge structures of compact hyperkähler manifolds [PDF]

, 2019
The purpose of this note is to give an account of a well-known folklore result: the Hodge structure on the second cohomology of a compact hyperk\"ahler manifold uniquely determines Hodge structures on all higher cohomology groups.
A. Soldatenkov
semanticscholar   +1 more source

MBM classes and contraction loci on low-dimensional hyperkähler manifolds of K3${}^{[n]}$ type [PDF]

Algebraic Geometry, 2019
An MBM locus on a hyperkahler manifold is the union of all deformations of a minimal rational curve with negative self-intersection. MBM loci can be equivalently defined as centers of bimeromorphic contractions.
E. Amerik, M. Verbitsky
semanticscholar   +1 more source

Mordell-Weil Groups of a Hyperkahler Manifold—A Question of F. Campana Dedicated to Professor Heisuke Hironaka on his 77-th birthday

, 2008
Among other things, we show that Mordell-Weil groups of finitely many different abelian fibrations of a hyperkahler manifold have essentially no relation, as its bira- tional transformation.
K. Oguiso
semanticscholar   +1 more source

Collapsing hyperkähler manifolds [PDF]

, 2017
Given a projective hyperkahler manifold with a holomorphic Lagrangian fibration, we prove that hyperkahler metrics with volume of the torus fibers shrinking to zero collapse in the Gromov-Hausdorff sense (and smoothly away from the singular fibers) to a ...
Valentino Tosatti, Yuguang Zhang
semanticscholar   +1 more source

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, Vicente Cortés, Jan Gregorovič   +2 more
wiley   +1 more source

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
wiley   +1 more source