We show that the Kahler-Ricci flow on an algebraic manifold of positive Kodaira dimension and semi-ample canonical line bundle converges to a unique canonical metric on its canonical model. It is also shown that there exists a canonical measure of analytic Zariski decomposition on an algebraic manifold of positive Koda…
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48 results for “canonical”
In this article we construct a canonical Kähler-Einstein current on a LC (log canonical) pairs of log general type as the limit of a sequence of canonical Kähler-Einstein currents on KLT(Kawamata log terminal) pairs of log general type. We call the volume form associated with the canonical Kähler-Einstein current the c…
New Hamiltonian Monte Carlo method for non-canonical dynamics.
problem Incompatibility of canonical symplectic structure with non-canonical dynamics.
method Developed a framework for Hamiltonian Monte Carlo using non-canonical symplectic structures with implicit integration.
result Non-canonical Hamiltonian Monte Carlo provides sampling advantages.
The paper finds canonical triangulations for specific 3-manifolds.
problem Finding canonical decompositions for cusped hyperbolic 3-manifolds.
method Showed local convexity at every face of the geometric triangulation.
result Found canonical triangulations for Dehn fillings of the Borromean rings link complement and related manifolds.
The paper defines and studies canonical parameters on surfaces in 4D space.
problem Understanding surfaces in 4D space without minimal points.
method Defining and proving existence of canonical principal parameters.
result Surfaces in 4D space are uniquely determined by four functions satisfying partial differential equations.
Counterexample disproves log canonical Beauville--Bogomolov decomposition.
problem Disproving the log canonical Beauville--Bogomolov decomposition.
method Constructing a specific log canonical, K-trivial variety with non-birational fibers.
result Provides a counterexample to the Beauville--Bogomolov decomposition in the log canonical setting.
For a submanifold M in a Euclidean space, the tangential component x^T of the position vector field x of M is the most natural vector field tangent to the Euclidean submanifold, called the canonical vector field of M. In this article, first we prove that the canonical vector field of every Euclidean submanifold is alwa…
Canonical correlation analysis was proposed by Hotelling [6] and it measures linear relationship between two multidimensional variables. In high dimensional setting, the classical canonical correlation analysis breaks down. We propose a sparse canonical correlation analysis by adding l1 constraints on the canonical vec…
Paper classifies compact symmetric triads using double Satake diagrams and canonical forms.
problem Classifying compact symmetric triads.
method Introducing double Satake diagrams and canonical forms, proving their existence and properties.
result Existence and properties of canonical forms for compact simple symmetric triads.
Canonical connections and algebraic Wanas solitons of three-dimensional Lorentzian Lie groupsmath.DG
The paper classifies solitons on specific Lie groups.
problem Classifying solitons on three-dimensional Lorentzian Lie groups.
method Computing Wanas tensor and defining algebraic Wanas solitons.
result Classification of algebraic Wanas solitons on specific Lie groups.
The covariant canonical formalism is a covariant extension of the traditional canonical formalism of fields. In contrast to the traditional canonical theory, it has a remarkable feature that canonical equations of gauge theories or gravity are not only manifestly Lorentz covariant but also gauge covariant or diffeomorp…
Study orders of canonical bundles over graph configuration spaces.
problem Determining bundle orders for planar and nonplanar graphs.
method Analyzing configuration spaces of graphs to find bundle orders.
result Bundle orders are 2 for planar and 4 for nonplanar graphs.
Using the fact that any minimal strongly regular surface carries locally canonical principal parameters, we obtain a canonical representation of these surfaces, which makes more precise the Weierstrass representation in canonical principal parameters. This allows us to describe locally the solutions of the natural part…
In this paper many classes of sets of matrices with entries in F (F=R, F=C, F=H) are introduced. Each class with the corresponding topology determines a real analytical, complex or symplectic manifold for F=R, F=C or F=H respectively. Any such family is called to be a set of canonical forms of matrices. The constructio…
Introduces a new canonical connection for Riemannian manifolds and proves Frobenius theorem geometrically.
problem Geometric proof of the Frobenius theorem on Riemannian manifolds.
method Introduces a new canonical connection and applies it to prove the Frobenius theorem.
result Geometric proof of the Frobenius theorem.
Explains BV Laplacian on half-densities in simple terms.
problem None explicitly stated; focuses on explanation.
method Didactical review of BV Laplacian on half-densities.
result Explains BV Laplacian concept in plain language.
Study complex solvmanifolds with trivial canonical bundle and hypercomplex geometry.
problem Characterize and produce examples of complex solvmanifolds with trivial canonical bundle.
method Characterize invariant trivializing sections using Koszul 1-form, provide algebraic obstructions, and exhibit specific examples.
result New examples of complex solvmanifolds with trivial canonical bundle and algebraic obstructions for triviality.
In this article, we construct the canonical semipositive current or the canonical measure ( the potential of the canonical semipositive current) on a smooth projective variety of nonnegative Kodaira dimension in terms of a dynamical system of Bergman kernels. This current is considered to be a generalization of a Kä…
Canonical connections and algebraic Ricci solitons of three-dimensional Lorentzian Lie groupsmath.DG
In this paper, we compute canonical connections and Kobayashi-Nomizu connections and their curvature on three-dimensional Lorentzian Lie groups with some product structure. We define algebraic Ricci solitons associated to canonical connections and Kobayashi-Nomizu connections. We classify algebraic Ricci solitons assoc…
Canonical correlation analysis is a family of multivariate statistical methods for the analysis of paired sets of variables. Since its proposition, canonical correlation analysis has for instance been extended to extract relations between two sets of variables when the sample size is insufficient in relation to the dat…
We describe which knots can be obtained as cycles in the canonical book representation of K_n, the complete graph on n vertices. We show that the canonical book representation of K_n contains a Hamiltonian cycle that is a composite knot if and only if n>11 and we show that when p and q are relatively prime, the (p,q) t…
We study the geometry of the canonical connection on a quasi-Kaehler manifold with Norden metric. We consider the cases when the canonical connection has Kaehler curvature tensor and parallel torsion, and derive conditions for an isotropic-Kaehler manifold. We give the relation between the canonical connection, the B-c…
Flow analysis leads to metric completion in Kähler geometry.
problem Analyzing Kähler-Ricci flows on compact manifolds.
method Normalized Kähler-Ricci flow convergence to Gromov-Hausdorff limits.
result Metric completion of twisted Kähler-Einstein metric.
Computes canonical heights for arithmetic log surfaces using Hurwitz zeta function.
problem Computing canonical heights for arithmetic log surfaces.
method Introduces a canonical height and uses limits of periods to compute it.
result Explicit formulas for canonical heights of arithmetic log surfaces, including (P_1,D).
Canonical framings and stable framings for the tangent bundle of a spin 3-manifold are introduced, and illustrated by a number of familiar examples. Methods for constructing canonical framings, and for comparing them with other naturally defined framings, are discussed.
The paper introduces canonical parameters for marginally trapped surfaces in Minkowski space.
problem Determining marginally trapped surfaces in Minkowski space.
method Introducing canonical parameters and proving existence and uniqueness theorems.
result Every marginally trapped surface is determined by three smooth functions.
The paper provides a combinatorial criterion for realizing tropical pluri-canonical divisors.
problem Determining when a tropical pair corresponds to a smooth algebraic curve with a pluri-canonical divisor.
method Introducing tropical normalized covers and reducing the problem to their realizability.
result Generalizes previous work on tropical canonical divisors and incorporates recent progress on -differentials.
We prove that the mirror map is trivial for the canonical formal families of Calabi-Yau varieties constructed by Gross and the second author. In other words, the natural coordinate in a canonical Calabi-Yau family is a canonical coordinate in the sense of Hodge theory. This implies that the higher weight periods direct…
Two Comments on "Laplace comparison on Kahler Ricci flow and convergence (arXiv:2509.14820v1)"math.DG
Clarifies definition of polarized canonical radius in Kahler Ricci flow.
problem Unclear definition of polarized canonical radius in Kahler Ricci flow.
method Clarification of the definition.
result Clarified definition of polarized canonical radius.
We construct a canonical basis of two-cycles, on a surface, in which the intersection form takes the canonical form . The basic elements are realized by formal sums of smooth submanifolds.
We calculate the monodromies of the canonical Lefschetz pencils on a pair of homeomorphic Horikawa surfaces. We show in particular that the (pluri)canonical pencils on these surfaces have the same monodromy groups, and are related by a "partial twisting" operation.
The existence of Kähler-Einstein metrics on a compact Kähler manifold has been the subject of intensive study over the last few decades, following Yau's solution to Calabi's conjecture. The Ricci flow, introduced by Richard Hamilton has become one of the most powerful tools in geometric analysis. We study the Kähler-Ri…
Constructs Kahler-Einstein metrics near isolated log canonical singularities.
problem Constructing metrics near singularities in complex geometry.
method Constructs Kahler-Einstein metrics with negative scalar curvature near isolated log canonical singularities.
result Metrics are complete near the singularity if the underlying space has complex dimension 2 or if the singularity is smoothable.
The paper studies fundamental groups of compact Kahler varieties with nef anti-canonical bundles.
problem Understanding the fundamental groups of compact Kahler varieties with specific properties.
method Application of geometric analytic theory of Kahler spaces and study of Albanese maps.
result The fundamental group of compact Kahler varieties with nef anti-canonical bundle is almost Abelian.
A Seifert surface for a knot K is called canonical if it can be built by applying Seifert's algorithm to some projection of K. The canonical genus of K is the smallest genus of a surface so obtained. In this paper we show that there is a bound on the volume of a hyperbolic knot which admits a canonical surface of genus…
This article considers the problem of sparse estimation of canonical vectors in linear discriminant analysis when . Several methods have been proposed in the literature that estimate one canonical vector in the two-group case. However, canonical vectors can be considered if the number of groups is . In…
Lin and Sjamaar have used symplectic Hodge theory to obtain canonical equivariant extensions for Hamiltonian actions on closed symplectic manifolds that have the strong Lefschetz property. Here we obtain canonical equivariant extensions much more generally by means of classical Hodge theory.
The paper extends deformation theory to Calabi-Yau varieties with isolated log canonical singularities.
problem Deformation theory of Calabi-Yau varieties with log canonical singularities.
method Study of higher Du Bois and rational singularities, focusing on 0-liminal singularities.
result Existence of first order smoothings for isolated 0-liminal hypersurface singularities.
Characterizes braid types and estimates twist coefficients.
problem Understanding braid types and their properties.
method Birman-Ko-Lee left canonical form of braids.
result Characterization of almost strongly quasipositive braids and estimates of fractional Dehn twist coefficient.
Surveying recent work on Kähler metrics and algebraic variety stability.
problem Understanding canonical Kähler metrics on algebraic varieties.
method Analyzing recent developments in algebraic geometry.
result Relation between canonical Kähler metrics and stability in algebraic geometry.
Counterexample disproves conjectures about log canonical thresholds.
problem Conjectures about log canonical thresholds were disproved.
method Provided a counterexample to both conjectures.
result Conjectures about log canonical thresholds are false.
Study pseudoholomorphic maps using canonical connection.
problem Characterize pseudoholomorphic maps between almost Hermitian manifolds.
method Use canonical connection and Bochner formulas to derive estimates and theorems.
result Obtained -estimate of canonical second fundamental form and Liouville type theorems.
A new method estimates conditional canonical correlations using random forests.
problem Estimating relationships between two sets of variables given covariates.
method Random Forest with Canonical Correlation Analysis (RFCCA)
result RFCCA provides accurate canonical correlation estimations and well-controlled Type-1 error.
We study global log canonical thresholds of del Pezzo surfaces.
For multiple multivariate data sets, we derive conditions under which Generalized Canonical Correlation Analysis (GCCA) improves classification performance of the projected datasets, compared to standard Canonical Correlation Analysis (CCA) using only two data sets. We illustrate our theoretical results with simulation…
Graph Canonical Correlation Analysis improves CCA for multiomics datasets.
problem Limited ability of conventional CCA methods to incorporate structured patterns in cross-correlation matrices.
method Graph Canonical Correlation Analysis (gCCA) calculates canonical correlations based on the graph structure of cross-correlation matrices.
result gCCA outperforms competing CCA methods in simulations and multiomics dataset analysis.
Introduces integer-valued Heegaard Floer theory with canonical orientations.
problem Defining and proving properties of Heegaard Floer homology over integers.
method Using canonical orientations from coupled Spin structures, proving naturality and surgery exact triangle.
result Established integer-valued Heegaard Floer theory and proved its properties.
This note describes a canonical way to orient the Heisenberg 3-manifold.