Results 51 to 60 of about 261,915 (134)

Corrigendum: Finiteness of polarized K3 surfaces and hyperkähler manifolds

, 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

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
wiley   +1 more source

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
wiley   +1 more source

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
wiley   +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

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
wiley   +1 more source

Hyper-K\"ahler Fourfolds Fibered by Elliptic Products

, 2018
Every fibration of a projective hyper-K\"ahler fourfold has fibers which are Abelian surfaces. In case the Abelian surface is a Jacobian of a genus two curve, these have been classified by Markushevich. We study those cases where the Abelian surface is a
Kamenova, Ljudmila
core   +1 more source

Abundance for varieties with many differential forms

, 2018
We prove that the abundance conjecture holds on a variety $X$ with mild singularities if $X$ has many reflexive differential forms with coefficients in pluricanonical bundles, assuming the Minimal Model Program in lower dimensions.
Lazić, Vladimir, Peternell, Thomas
core   +1 more source

Systems of symplectic forms on four-manifolds [PDF]

, 2012
We study almost Hermitian 4-manifolds with holonomy algebra, for the canonical Hermitian connection, of dimension at most one. We show how Riemannian 4-manifolds admitting five orthonormal symplectic forms fit therein and classify them. In this set-up we
Chiossi, SImon G., Nagy, Paul-Andi
core   +1 more source

Integral cohomology of the Generalized Kummer fourfold

, 2017
We describe the integral cohomology of the Generalized Kummer fourfold giving an explicit basis, using Hilbert scheme cohomology and tools developed by Hassett and Tschinkel.
Kapfer, Simon, Menet, Grégoire
core   +2 more sources