Classifies special types of 4D spaces.
problem Classifying non-reductive 4D spaces.
method Classification based on conformal Einstein manifolds.
result Classification of non-reductive 4D homogeneous conformally Einstein manifolds.
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18 results for “non-reductive”
Study extends Kobayashi's method to non-reductive subgroups for homogeneous spaces.
problem Existence of compact Clifford-Klein forms in homogeneous spaces.
method Extend Kobayashi's method to non-reductive subgroups and compare Cartan projections and non-compact dimensions.
result Examples of homogeneous spaces without compact Clifford-Klein forms.
Classifies special hypersurfaces in specific types of manifolds.
problem Characterizing geometric structures in non-reductive homogeneous spaces.
method Classification of parallel and totally geodesic hypersurfaces.
result Found a complete classification of these hypersurfaces.
A method, due to Élie Cartan, is used to give an algebraic classification of the non-reductive homogeneous pseudo-Riemannian manifolds of dimension four. Only one case with Lorentz signature can be Einstein without having constant curvature, and two cases with (2,2) signature are Einstein of which one is Ricci-flat. If…
Counterexample disproves conjecture about Fano varieties with non-reductive automorphisms.
problem Disproving the conjecture about Loewy filtrations destabilizing non-reductive Fano varieties.
method Constructing a counterexample to the Loewy filtration conjecture.
result Found a Fano variety with non-reductive automorphism group that does not destabilize Loewy filtration.
The paper extends invariant theory to non-compact and non-reductive actions, classifying four regimes.
problem Extending invariant theory to non-compact and non-reductive actions.
method Examined two specific settings: discrete subgroups of Lorentz group acting on and cocompact actions on smooth manifolds.
result Classification of invariant-theoretic regimes into four categories, identifying boundaries of Hilbert--Weyl and Schwarz theorems.
We study the K-stability of a polarised variety with non-reductive automorphism group. We associate a canonical filtration of the co-ordinate ring to each variety of this kind, which destabilises the variety in several examples which we compute. We conjecture this holds in general. This is an algebro-geometric analogue…
We introduce an analogue in hyperkahler geometry of the symplectic implosion, in the case of SU(n) actions. Our space is a stratified hyperkahler space which can be defined in terms of quiver diagrams. It also has a description as a non-reductive geometric invariant theory quotient.
It is shown that, in the Gromov space of isometry classes of pointed proper metric spaces, the equivalence relations defined by existence of coarse quasi-isometries or being at finite Gromov-Hausdorff distance, cannot be reduced to the equivalence relation defined by any Polish action.
New representation of curves helps prove complex geometry result.
problem Understanding cohomologically stable curves in projective space.
method Using commuting matrix polynomials to represent curves and show isomorphism to hyperkähler quotient.
result Hilbert scheme isomorphic to a hyperkähler quotient.
Reconstruct Lie algebra from subalgebra and quotient representation.
problem Reconstructing Lie algebra from subalgebra and quotient representation.
method Using Lie algebra cohomology to reconstruct Lie algebra.
result Found all ingredients for building non-reductive Klein geometries.
Develops a new geometric framework for quantum metrics.
problem Quantum metric generalization for pure two-qubit states.
method Support-projected Petz monotone geometry for pure two-qubit families.
result Strictly generalizes SLD/Bures case and includes other metrics.
For two positive integers m and n, we let be the open convex cone in consisting of positive definite n x n real symmetric matrices and let be the set of all m x n real matrices. In this article, we investigate differential operators on the non-reductive ma…
Weighted projective embeddings, stability of orbifolds and constant scalar curvature Kähler metricsmath.AG
We embed polarised orbifolds with cyclic stabiliser groups into weighted projective space via a weighted form of Kodaira embedding. Dividing by the (non-reductive) automorphisms of weighted projective space then formally gives a moduli space of orbifolds. We show how to express this as a reductive quotient and so a GIT…
Develops a new framework for generalized Ricci flow on Lie groups.
problem Global existence and geometric properties of Ricci flow on Lie groups.
method Inspired by Lauret's bracket flow, studies generalized Ricci flow on discrete quotients of Lie groups.
result Establishes global existence on solvmanifolds in arbitrary dimensions.
Constructs geometric models for moduli spaces of Higgs bundles over Riemann sphere.
problem Construction of moduli spaces for Higgs bundles with specific properties.
method Elementary geometric and combinatorial techniques, focusing on orbit stability of automorphism groups.
result Explicit geometric models for moduli spaces of parabolic Higgs bundles over Riemann sphere.
Study calculates Ricci bounds for special Fano manifolds.
problem Computing Ricci bounds for specific Fano manifolds.
method Using barycenter of moment polytopes with Duistermaat-Heckman measure.
result Greatest Ricci lower bounds can be arbitrarily close to zero.
New method for moduli spaces of twisted quiver representations and Higgs bundles.
problem Computing moduli spaces of twisted quiver representations and Higgs bundles.
method Extending twisted A-type quiver representations to any genus using Hitchin stability and deformation theory.
result Explicit geometric identifications of moduli spaces of twisted representations of argyle quivers on .