Results 21 to 30 of about 95,172 (100)

A characterization of compact locally conformally hyperkähler manifolds [PDF]

, 2019
We give an equivalent definition of compact locally conformally hyperkähler manifolds in terms of the existence of a nondegenerate complex two-form with natural properties. This is a conformal analogue of Beauville's theorem stating that a compact Kähler
Otiman, A., Otiman A., Ornea, L., Ornea L.   +3 more
core   +1 more source

The period-index problem for hyperkähler manifolds [PDF]

We conjecture that every unramified Brauer class $α\in \text{Br}(X)$ on a projective hyperkähler manifold $X$ satisfies $\text{ind}(α)\mid\text{per}(α)^{\dim(X)/2}$.
Huybrechts, Daniel
core   +2 more sources

Hyperkähler manifolds of Jacobian type [PDF]

, 2016
In this paper we define the notion of a hyperkähler manifold (potentially) of Jacobian type. If we view hyperkähler manifolds as “abelian varieties”, then those of Jacobian type should be viewed as “Jacobian varieties”.
Shen, M.
core   +1 more source

Kuga–Satake Construction on Families of K3 Surfaces of Picard Rank 14

Mathematische Nachrichten, Volume 299, Issue 8, Page 1894-1916, August 2026.
ABSTRACT The isometry between the type IV6 and the type II4 hermitian symmetric domains suggests a possible relation between suitable moduli spaces of K3 surfaces of Picard rank 14 and of polarized abelian 8‐folds with totally definite quaternion multiplication. We show how this isometry induces a geometrically meaningful map between such moduli spaces
Flora Poon
wiley   +1 more source

Inducing Coverings on Hilbert Schemes

Mathematische Nachrichten, Volume 299, Issue 8, Page 2177-2190, August 2026.
ABSTRACT We find an explicit geometric description of all coverings of Hilb2(Σ)$\operatorname{Hilb}^{2}(\Sigma)$ when Σ$\Sigma$ is a normal, complex, quasi‐projective surface with finite fundamental group. We then apply this construction to show that if Σ$\Sigma$ is an irreducible symplectic surface then Hilb2(Σ)$\operatorname{Hilb}^{2}(\Sigma)$ is an ...
Lucas Li Bassi, Filippo Papallo
wiley   +1 more source

Hyperkähler and quaternionic Kähler geometry [PDF]

, 2016
A quaternion-Hermitian manifold, of dimension at least 12, with closed fundamental 4-form is shown to be quaternionic Kähler. A similar result is proved for 8-manifolds.

core   +1 more source

Lefschetz decompositions of Kudla–Millson theta functions

Proceedings of the London Mathematical Society, Volume 133, Issue 2, August 2026.
Abstract In the 1980s Kudla and Millson introduced a theta function in two variables. It behaves as a Siegel modular form with respect to the first variable, and is a closed differential form on an orthogonal Shimura variety X$X$ with respect to the other variable. We prove that the Lefschetz decomposition of the cohomology class of that theta function
Jan Hendrik Bruinier, Riccardo Zuffetti
wiley   +1 more source

Hyperkähler manifolds of curves and l-hypercomplex structures [PDF]

, 2018
In this work we focus our attention on the description of hyperkähler manifolds that arise as moduli spaces of curves inside twistor spaces that admit a fibration on the tangent bundle to the Riemann sphere.
Lora Lamia Donin, Niccolò
core   +1 more source

Simple normal crossing Kähler–Einstein metrics and RCD spaces

Bulletin of the London Mathematical Society, Volume 58, Issue 7, July 2026.
Abstract We show that Kähler–Einstein metrics with cone singularities along simple normal crossing (SNC) divisors define Riemannian Curvature Dimension (RCD) spaces, both in the compact setting and in certain non‐compact cases, thereby producing many examples of Einstein RCD spaces. In particular, we show the existence of smooth non‐compact 4‐manifolds
Martin de Borbon, Cristiano Spotti
wiley   +1 more source

Cohomogeneity‐one solitons in Laplacian flow: Local, smoothly‐closing and steady solitons

Journal of the London Mathematical Society, Volume 113, Issue 6, June 2026.
Abstract We initiate a systematic study of cohomogeneity‐one solitons in Bryant's Laplacian flow of closed G2$\text{G}_2$‐structures on a 7‐manifold, motivated by the problem of understanding finite‐time singularities of that flow. Here, we focus on solitons with symmetry groups Sp(2)${\rm Sp}(2)$ and SU(3)${\rm SU}(3)$; in both cases, we prove the ...
Mark Haskins, Johannes Nordström
wiley   +1 more source