arXiv research

Study shows convergence of cscK surfaces in Hilbert scheme.

The paper introduces $μ$K-stability for polarized schemes and develops equivariant calculus.

Given a one parameter flat family of polarized algebraic varieties, we show that any K-stable limit is unique. In particular, moduli spaces of K-stable polarized varieties are automatically Hausdorff when they exist. We also give a characterization of K-stable limits in terms of the CM line bundle, and some application…

The formulation of Geometric Quantization contains several axioms and assumptions. We show that for real polarizations we can generalize the standard geometric quantization procedure by introducing an arbitrary connection on the polarization bundle. The existence of reducible quantum structures leads to considering the…

In this work, we introduce a deep learning-based polar code construction algorithm. The core idea is to represent the information/frozen bit indices of a polar code as a binary vector which can be interpreted as trainable weights of a neural network (NN). For this, we demonstrate how this binary vector can be relaxed t…

Improves MCMC performance with adaptive affine transformations.

The holomorphic invariants introduced by Futaki as obstruction to the asymptotic Chow semistability are studied by an algebraic-geometric point of view and are shown to be the Mumford weights of suitable line bundles on the Hilbert scheme. These invariants are calculated in two special cases. The first is a projective …

The paper analyzes word embeddings and their failure to distinguish polarized terms.

We classify the polar actions on the complex hyperbolic plane up to orbit equivalence. Apart from the trivial and transitive polar actions, there are five polar actions of cohomogeneity one and four polar actions of cohomogeneity two.

Study polar actions on Damek-Ricci spaces, proving existence and finding examples.

The paper studies how Kähler polarizations degenerate to mixed polarizations on toric varieties.

Polarized and $G$-polarized CR manifolds are smooth manifolds endowed with a double structure: a real foliation $\Cal F$ (given by the action of a Lie group $G$ in the $G$-polarized case) and a transverse CR distribution $(E,J)$. Polarized means that $(E,J)$ is roughly speaking invariant by $\Cal F$. Both structures ar…

A polarity of a projective plane is a map, often assumed to be involutive, mapping a generic point to a generic line and reciprocally. The most classical polarity is the polarity with respect to a conic, but other exist: the harmonic polarity with respect to a triangle, the polarities with respect to high-degree algebr…

The generic fiber of a Lagrangian fibration on an irreducible holomorphic symplectic manifold is an abelian variety. Associate a polarization type to such Lagrangian fibrations coming from polarizations on a generic fiber. We prove that this polarization type is constant in families of Lagrangian fibrations. Further, w…

We study the limiting case of the Krichever construction of orthogonal curvilinear coordinate systems when the spectral curve becomes singular. We show that the case when the curve is reducible and all its irreducible components are rational curves the construction procedure reduces to solving systems of linear equatio…

Paper uses ResUNet-CMB to reconstruct cosmic polarization rotation from CMB data.

Unified framework for observables in n-plectic geometry.

The study introduces polarization of generalized Nijenhuis torsions and their relevance in operator fields.

Classifies polar foliations on symmetric spaces.

Assume that a projective variety together with a polarization is uniformly K-stable. If the polarization is canonical or anti-canonical, then the projective variety is uniformly K-stable with respects to any polarization sufficiently close to the original polarization.

Classifies totally geodesic submanifolds and polar actions on Stiefel manifolds.

The main result of this paper is that a polar action on a compact irreducible homogeneous Kaehler manifold is coisotropic. This is then used to give new examples of polar actions and to classify coisotropic and polar actions on quadrics.

Classifies hexagonal circular 3-webs with cubic polar curves.

POLAR framework interprets word embeddings using polar opposites.

Study empty polar varieties' impact on singular function-germs.

For complex projective manifolds we introduce polar homology groups, which are holomorphic analogues of the homology groups in topology. The polar k-chains are subvarieties of complex dimension k with meromorphic forms on them, while the boundary operator is defined by taking the polar divisor and the Poincare residue …

Totally geodesic sections found in polar actions.

We prove a criterion for an isometric action of a Lie group on a Riemannian manifold to be polar. From this criterion, it follows that an action with a fixed point is polar if and only if the slice representation at the fixed point is polar and the section is the tangent space of an embedded totally geodesic submanifol…

The imbalance of buying and selling functions profoundly in the formation of market trends, however, a fine-granularity investigation of the imbalance is still missing. This paper investigates a unique transaction dataset that enables us to inspect the imbalance of buying and selling on the man-times level at high freq…

We show that simply connected Riemannian homogeneous spaces of compact semisimple Lie groups with polar isotropy actions are symmetric, generalizing results of Fabio Podesta and the third named author. Without assuming compactness, we give a classification of Riemannian homogeneous spaces of semisimple Lie groups whose…

Carnot groups can be polarized if they have specific coordinate systems.

Polar manifolds are Riemannian G-manifolds admitting a "section", i.e., a complete submanifold passing through every orbit and doing so orthogonally. We consider compact simply-connected polar manifolds and achieve an equivariantly diffeomorphic classification in dimensions 5 or less. As an application, we determine wh…

The paper bounds abnormal and Goh-abnormal sets for metabelian Lie groups with polarizations.

This paper deals with skew ruled surfaces in the Euclidean space $\mathbb{E}^{3}$ which are equipped with polar normalizations, that is, relative normalizations such that the relative normal at each point of the ruled surface lies on the corresponding polar plane. We determine the invariants of a such normalized ruled …

In this paper, we generalize the polar transforms of spacelike isothermic surfaces in $Q^4_1$ to n-dimensional pseudo-Riemannian space forms $Q^n_r$. We show that there exist $c-$polar spacelike isothermic surfaces derived from a spacelike isothermic surface in $Q^n_r$, which are into $S^{n+1}_r(c)$, $H^{n+1}_{r-1}(c)$…

Classifies polar actions on 3D homogeneous spaces.

We give a simple sufficient condition for K-stability of polarized del Pezzo surfaces and for the existence of a constant scalar curvature Kahler metric in the Kahler class corresponding to the polarization.

We classify infinitesimally polar actions on compact Riemannian symmetric spaces of rank one. We also prove that every polar action on one of those spaces has the same orbits as an asystatic action.

Investigates polar tangential angles of curves and their monotonicity.

The paper introduces polarizations in symplectic and orthogonal settings.

Classifies foliations on specific symmetric spaces.

In this paper, assuming that a polarized algebraic manifold $(X,L)$ is strongly K-stable, we shall show that the polarization class $c_1(L)$ admits a constant scalar curvature Kaehler metric.

Proved inequality for anti-self-polar polytopes.

New method shows unitarity in quantization for toric manifolds.

The paper introduces a method to make neural networks more robust to adversarial attacks.

Introduces Polar Depth for analyzing multivariate heavy-tailed data extremes.

Paper uses polar field data to improve solar flare prediction accuracy.

An asymptotic formula for the Tian-Paul CM-line of a flat family blown-up at a flat closed sub-scheme is given. As an application we prove that the blow-up of a polarized manifold along a (relatively) Chow-unstable submanifold admits no (extremal) constant scalar curvature Kahler metrics in classes making the exception…