New 3D shapes can't be split into torus pieces.
problem 3D shapes without torus decompositions.
method Recursive definition from compact 3-manifolds.
result Examples of 3D shapes failing torus decomposition.
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48 results for “3D toric manifolds”
A new formula calculates contributions of tropical curves to Gromov-Witten invariants in 3D.
problem Calculating contributions of tropical curves to Gromov-Witten invariants in 3D.
method Developed a new formula with modified contributions at trivalent vertices.
result A simple formula for calculating Gromov-Witten invariants in 3D.
Toric Vaisman Manifoldsmath.DG
The paper explores toric Vaisman manifolds and their connections to Sasaki and Kähler geometry.
problem Understanding the geometric relationships between Vaisman, Sasaki, and Kähler manifolds in the toric context.
method Introducing and analyzing toric Vaisman structures, showing relationships between minimal coverings and associated Sasaki manifolds, and proving conditions for toricity.
result Toric Vaisman manifolds have a close relationship with toric Sasaki manifolds, and vice versa, under specific conditions.
We introduce the cutting construction of possibly non-compact symplectic toric manifolds, in particular, toric symplectic cones that correspond to a weakly convex good cone. Since the symplectization of a toric contact manifold is a toric symplectic cone, we can also construct toric contact manifolds that correspond to…
Proves Yau-Tian-Donaldson conjecture for toric manifolds and bundles.
problem Yau-Tian-Donaldson conjecture for toric manifolds and bundles.
method Filtration approach to prove the conjecture.
result Proves Yau-Tian-Donaldson conjecture for toric manifolds and bundles.
This paper provides a new method to construct -symplectic toric manifolds from toric manifolds.
problem Classifying and constructing -symplectic toric manifolds.
method A new method to construct -symplectic toric manifolds from toric manifolds.
result This new method allows for the decomposition of -symplectic toric manifolds into toric manifolds.
Toric hyperk{ä}hler manifolds are quaternion analog of toric varieties. Bielawski pointed out that they can be glued by cotangent bundles of toric varieties. Following his idea, viewing both toric varieties and toric hyperk{ä}her manifolds as GIT quotients, we first establish geometrical criteria for the semi-stable po…
Study on mean Euler characteristic of Gorenstein toric contact manifolds.
problem Calculating the mean Euler characteristic of Gorenstein toric contact manifolds.
method Using the relationship between mean Euler characteristic and the normalized volume of the toric diagram, and applying results from Batyrev and Dais.
result Twice the mean Euler characteristic of a Gorenstein toric contact manifold equals the Euler characteristic of any crepant toric symplectic filling.
Study on compact toric locally conformally Kähler manifolds, finding specific properties.
problem Characterizing properties of compact toric locally conformally Kähler manifolds.
method Analyzing Kodaira dimension, using specific examples and mappings.
result Kodaira dimension is -∞ for underlying complex manifolds, and specific properties for surfaces and Vaisman manifolds.
New SKT manifolds created using toric geometry.
problem Creating SKT manifolds.
method Using toric geometry and -construction.
result Infinite families of SKT manifolds produced.
Study characterizes toric LCK manifolds, proving conjecture and showing differences from symplectic case.
problem Characterizing compact toric locally conformally Kähler manifolds.
method Proves conjecture about toric LCK manifolds, constructs examples to show differences from symplectic case.
result Proves a conjecture about toric LCK manifolds and shows differences from symplectic case.
Constructs scalar-flat Kähler metrics on toric symplectic manifolds.
problem Creating scalar-flat Kähler metrics on toric symplectic manifolds.
method Explicit construction and alternative construction with conical singularity.
result Explicit construction of scalar-flat Kähler metrics on toric symplectic manifolds.
A series of examples of toric Sasaki-Einstein 5-manifolds is constructed. These are submanifolds of toric 3-Sasaki 7-manifolds and such a Sasaki-Einstein 5-manifold corresponds uniquely to a toric 3-Sasaki 7-manifold. This produces examples of quasi-regular Sasaki-Einstein structures on every #k(S^2 xS^3), for k odd. T…
Cylindrical contact homology linked to Ehrhart polynomials and Chen-Ruan cohomology.
problem Contact invariants of Q-Gorenstein toric contact manifolds.
method Relationships between cylindrical contact homology and Ehrhart polynomials, Chen-Ruan cohomology.
result Cylindrical contact homology invariants linked to Ehrhart polynomials and Chen-Ruan cohomology.
Uniqueness of Kähler Ricci shrinkers proven on toric orbifolds.
problem Proving uniqueness of Kähler Ricci shrinkers on toric orbifolds.
method Extending results from toric manifolds to toric orbifolds.
result Uniqueness of Kähler Ricci shrinkers on toric orbifolds established.
Toric Kato manifoldsmath.AG
Study of special Kato manifolds derived from toric geometry.
problem Characterize and study properties of Kato manifolds.
method Construction from toric geometry, topological and analytical properties, combinatorial data, flat degenerations, Hermitian geometry.
result No Kato manifold supports balanced or pluriclosed metrics.
Toric contact manifolds defined in any dimension.
problem No specific problem stated; abstract focuses on definition.
method Description via labelled polytope in grassmannian.
result Toric contact manifolds in arbitrary codimension.
Toric actions in cosymplectic geometry linked to symplectomorphisms.
problem Understanding toric actions in cosymplectic geometry.
method Showed that compact toric cosymplectic manifolds are mapping tori of equivariant symplectomorphisms of toric symplectic manifolds.
result Compact toric cosymplectic manifolds are mapping tori of equivariant symplectomorphisms of toric symplectic manifolds.
New toric Fano manifolds found without extremal Kähler metrics.
problem Finding toric Fano manifolds without extremal Kähler metrics.
method Constructing specific toric Fano manifolds of dimensions 10 and n (n≥11) that do not admit extremal Kähler metrics.
result Existence of toric Fano manifolds of dimension 10 and higher that do not admit extremal Kähler metrics.
Study global geometry of toric nearly Kähler manifolds using multi-moment maps.
problem Global properties of toric nearly Kähler manifolds.
method Description using multi-moment maps, investigation of polynomial and radial solutions.
result Description of global geometry of toric nearly Kähler manifolds.
We give criterions for the existence of toric conical Kahler-Einstein and Kahler-Ricci soliton metrics on any toric manifold in relation to the greatest Ricci and Bakry-Emery-Ricci lower bound. We also show that any two toric manifolds with the same dimension can be joined by a continuous path of toric manifolds with c…
Solves a general problem for toric manifolds in Kaehler-Ricci solitons.
problem General problem stated by authors for toric manifolds in Kaehler-Ricci solitons.
method Proves that a Calabi extremal Kaehler-Ricci soliton on a compact toric Kaehler manifold is Einstein.
result Solves for the class of toric manifolds a general problem stated by the authors.
The geodesic flow of a Riemannian metric on a compact manifold is said to be toric integrable if it is completely integrable and the first integrals of motion generate a homogeneous torus action on the punctured cotangent bundle . If the geodesic flow is toric integrable, the cosphere bundle admit…
Quantizes -symplectic toric manifolds using -modules.
problem Quantization of -symplectic toric manifolds.
method Bohr-Sommerfeld quantization via -modules.
result Dimension of quantization coincides with signed count of integral points in moment polytope.
Computes Weyl group of Kähler toric manifold isometries.
problem Computing the Weyl group of Kähler toric manifold isometries.
method Analyzes the group of holomorphic isometries of a Kähler toric manifold with real analytic Kähler metric.
result Computed the Weyl group of the group of holomorphic isometries.
Direct proof of Danilov-type formula for toric origami manifolds.
problem Proving a Danilov-type formula for toric origami manifolds.
method Localization of Riemann-Roch number.
result Direct geometric proof of Danilov-type formula.
Moment polytope of toric exponential families is a projection of a simplex.
problem Understanding the geometry of exponential families in finite sample spaces.
method Toric torification and projection of higher-dimensional simplices.
result Moment polytope is a projection of a higher-dimensional simplex.
New metrics found on toric LCS manifolds.
problem Finding compatible complex structures on toric LCS manifolds.
method Proved a bijective correspondence between toric LCS manifolds and pairs .
result Compact toric LCS manifolds have a positive potential.
New submanifolds found in toric manifolds with specific actions.
problem Understanding submanifolds in toric manifolds with complex subtorus actions.
method Analyzing the closure of a complex subtorus in a toric manifold and its Hamiltonian action.
result The image of the moment map for the Hamiltonian subtorus action coincides with the image of the Delzant polytope.
Proves every equivariant vector bundle over toric manifolds is a Klyachko bundle.
problem Characterizing equivariant vector bundles over toric manifolds.
method Analyzes topological and smooth equivariant vector bundles over toric manifolds.
result Every equivariant vector bundle is a Klyachko bundle.
The paper examines stability conditions for toric manifolds using algebraic geometry.
problem Investigating stability conditions for toric manifolds in algebraic geometry.
method Using criteria for relative Chow and K-stability, the paper applies the Hibert-Mumford criterion and considers maximal torus actions and -actions.
result The paper provides a criterion for relative K-stability and instability of toric Fano manifolds and presents counter-examples of relative K-stable but asymptotically Chow unstable manifolds.
Almost toric manifolds form a class of singular Lagrangian fibered symplectic manifolds that is a natural generalization of toric manifolds. Notable examples include the K3 surface, the phase space of the spherical pendulum and rational balls useful for symplectic surgeries. The main result of the paper is a complete c…
Classifies equivariant vector bundles over toric manifolds.
problem Classifying vector bundles over toric manifolds.
method Klyachko-type classification over invariant affine charts.
result Generalizes Klyachko's classification of toric vector bundles.
In this paper, we discuss the relative -stability and the modified -energy associated to the Calabi's extremal metric on toric manifolds. We give a sufficient condition in the sense of convex polytopes associated to toric manifolds for both the relative -stability and the properness of modified -energy. In …
Uniform K-stability ensures existence of special metrics on toric manifolds.
problem Existence of conformally Kähler, Einstein-Maxwell metrics on toric manifolds.
method Introducing uniform K-stability and showing its equivalence to properness of relative K-energy.
result Uniform K-stability is necessary and sufficient for the existence of -extremal metrics on toric manifolds.
The paper derives a formula for Chow weights of toric blow-ups.
problem Chow weights of toric blow-ups.
method Combinatorial formula derived from toric manifold and Delzant polytope.
result Explicit formula for Chow weights of blow-ups.
Proof confirms condition for Kähler-Einstein metrics on toric Fano manifolds.
problem Existence of Kähler-Einstein metrics on toric Fano manifolds.
method Condition in terms of barycenters of polytopes.
result Necessary and sufficient conditions for existence of coupled Kähler-Einstein metrics and soliton solutions.
We show that any $(\C ^*)^n$-invariant stably complex structure on a topological toric manifold of dimension is integrable. We also show that such a manifold is weakly $(\C ^*)^n$-equivariantly isomorphic to a toric manifold.
Characterizes stable toric Fano manifolds using modified Ding functional.
problem Stability of toric Fano manifolds.
method Characterization through modified Ding functional and pseudo-boundedness analysis.
result Characterization of relative Ding stable toric Fano manifolds.
The paper solves a uniform Yau-Tian-Donaldson conjecture for toric manifolds.
problem Uniform Yau-Tian-Donaldson conjecture for polarized toric manifolds.
method Combinatorial sufficient condition for relative K-polystability.
result Uniform relative K-polystability condition established.
Criterion found for Kähler Einstein metrics on toric Fano manifolds.
problem Existence of Kähler Einstein metrics on toric Fano manifolds.
method Criterion based on uniform stability in GIT and properness of a functional.
result Complete criterion for existence of generalized Kähler Einstein metrics.
The paper constructs submanifolds with corners in Delzant polytopes from affine subspaces.
problem Understanding submanifolds with corners in Delzant polytopes.
method Constructing submanifolds with corners in Delzant polytopes from affine subspaces.
result Conditions for submanifolds with corners are equivalent to those for torus-equivariantly embedded toric manifolds.
Real Lagrangians in toric manifolds are classified by combinatorial data.
problem Classifying real Lagrangian submanifolds in toric symplectic manifolds.
method Established a real analog of the Delzant construction.
result Real Lagrangians in toric del Pezzo surfaces have all possible diffeomorphism types.
Strong formal properties for toric and homogeneous Kähler manifolds.
problem Understanding formal properties of Kähler manifolds.
method Analyzing rationally and strongly formal properties of toric and homogeneous Kähler manifolds.
result Toric and homogeneous Kähler manifolds are both rationally and strongly formal.
The paper analyzes solitonic components of toric manifolds.
problem Analyzing solitonic components of toric manifolds.
method Computing eigenfunctions of a solitonic complex Laplacian operator.
result Determination of solitonic decomposition of Fano toric manifolds.
The paper studies a generalized Pythagorean theorem on dually flat spaces via toric geometry.
problem Understanding the geometry of dually flat spaces and their toric Kähler manifolds.
method Introducing a dually flat structure and Bregman divergence on the boundary of toric Kähler manifolds.
result A continuity and generalized Pythagorean theorem for the divergence on the boundary.
On Lagrangian Tori in math.SG
Classifies toric fibers in .
problem Identify Hamiltonian isotopy of toric fibers.
method Comprehensive classification of toric fibers in FOOO's construction.
result Determines Hamiltonian isotopy of toric fibers.
The paper studies semistability in polarized toric manifolds and their divisors.
problem Semistability of polarized toric manifolds and their divisors.
method Combinatorial arguments and obstruction of semistability.
result Implication from asymptotic log Chow semistability to log K-semistability.