Results 31 to 40 of about 257,749 (139)

Teichmüller spaces and Torelli theorems for hyperkähler manifolds [PDF]

open access: yesMathematische Zeitschrift, 2019
Kreck and Yang Su recently gave counterexamples to a version of the Torelli theorem for hyperkählerian manifolds as stated by Verbitsky. We extract the correct statement and give a short proof of it.
E. Looijenga
semanticscholar   +1 more source

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

open access: yesAlgebraic 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

Canonical complex extensions of Kähler manifolds

open access: yesJournal 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

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

open access: yesInternational 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

On the Hodge structures of compact hyperkähler manifolds [PDF]

open access: yes, 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

Limit Mixed Hodge Structures of Hyperkähler Manifolds [PDF]

open access: yesMoscow Mathematical Journal, 2018
This note is inspired by the work of Deligne on the local behavior of Hodge structures at infinity. We study limit mixed Hodge structures of degenerating families of compact hyperk\"ahler manifolds.
A. Soldatenkov
semanticscholar   +1 more source

Curvature of quaternionic skew‐Hermitian manifolds and bundle constructions

open access: yesMathematische 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
wiley   +1 more source

Characteristic foliations — A survey

open access: yesBulletin 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

Subquadratic harmonic functions on Calabi‐Yau manifolds with maximal volume growth

open access: yesCommunications 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
wiley   +1 more source

Corrigendum: Finiteness of polarized K3 surfaces and hyperkähler manifolds

open access: yes, 2020
In the proof of Proposition 2.8 in [Huy18] we consider isometric embeddings φ : T (S0)  //T (S0)⊕ Z · e with φ(σ) ∈ C · σ⊕C · σ̄⊕C · e. At this point Lemma 2.5 is evoked, which, however, assumes the more restrictive and unrealistic condition (2.1) φC(σ)
D. Huybrechts
semanticscholar   +1 more source

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