Search
Search Results
-
On the Alesker-Verbitsky Conjecture on HyperKähler Manifolds
We solve the quaternionic Monge–Ampère equation on hyperKähler manifolds. In this way we prove the ansatz for the conjecture raised by Alesker and...
-
Lefschetz-type theorems for the effective cone on Hyperkähler varieties
In this paper we show some Lefschetz-type theorems for the effective cone of Hyperkähler varieties. In particular we are able to show that the...
-
Automorphisms of Hyperkähler Manifolds and Groups Acting on CAT(0) Spaces
We study groups of biholomorphic and bimeromorphic automorphisms of projective hyperkähler manifolds. Using a geometric action of these groups on...
-
-
-
The LLV Decomposition of Hyperkähler Cohomology and Applications to the Nagai Conjecture (After Green–Kim–Laza–Robles)
Following work of Green, Kim, Laza, and Robles, we discuss the structure and known cases of the decomposition of the cohomology of hyperkähler...
-
Fully Non-linear Elliptic Equations on Compact Manifolds with a Flat Hyperkähler Metric
Mainly motivated by a conjecture of Alesker and Verbitsky, we study a class of fully non-linear elliptic equations on certain compact hyperhermitian...
-
A bound on the second Betti number of hyperkähler manifolds of complex dimension six
Let M be an irreducible compact hyperkähler manifold of complex dimension six. Under an assumption on the Looijenga–Lunts–Verbitsky decomposition of...
-
On the Mumford–Tate conjecture for hyperkähler varieties
We study the Mumford–Tate conjecture for hyperkähler varieties. We show that the full conjecture holds for all varieties deformation equivalent to...
-
Complexified Hermitian Symmetric Spaces, Hyperkähler Structures, and Real Group Actions
There is a known hyperkähler structure on any complexified Hermitian symmetric space G / K , whose construction relies on identifying G / K with both a...
-
Contraction centers in families of hyperkähler manifolds
We study the exceptional loci of birational (bimeromorphic) contractions of a hyperkähler manifold M . Such a contraction locus is the union of all...
-
Hodge similarities, algebraic classes, and Kuga–Satake varieties
We introduce in this paper the notion of Hodge similarities of transcendental lattices of hyperkähler manifolds and investigate the Hodge conjecture...
-
Finiteness of stable Lagrangian fibrations
In this paper we survey some finiteness results of the deformation classes of hyperkähler Lagrangian fibrations, and we prove finiteness for stable...
-
GKM Graph Locally Modeled by \(T^{n}\times S^{1}\) -Action on \(T^{*}\mathbb {C}^{n}\) and Its Graph Equivariant Cohomology
We introduce a class of labeled graphs (with legs), which contains two classes of GKM graphs of 4n-dimensional manifolds with...
-
Hyperkähler cones and instantons on quaternionic Kähler manifolds
We present a novel approach to the study of Yang–Mills instantons on quaternionic Kähler manifolds, based on an extension of the harmonic space...
-
Rational Curves and MBM Classes on Hyperkähler Manifolds: A Survey
This paper deals with rational curves and birational contractions on irreducible holomorphically symplectic manifold. We survey some recent results...
-
K-Theory of Toric HyperKähler Manifolds
Let X be a toric hyperKähler manifold. The purpose of this note is to describe the topological K -ring K *( X ) of X . We give a presentation for the...
-
Solutions to Donaldson’s Hyperkähler Reduction on a Curve
We study an infinite-dimensional hyperkähler reduction introduced by Donaldson and associated with the constant scalar curvature equation on a...
