arXiv research

Study of height jumps in Ceresa cycle using asymptotic Hodge theory.

Researchers describe a Ceresa class for tropical and topological curves, linking algebraic and cohomological perspectives.

New invariant links graph structure to tropical curve properties.

New group-theoretic Johnson classes applied to curves with torsion Ceresa classes.

We construct natural Green forms for special cycles in orthogonal and unitary Shimura varieties, in all codimensions, and, for compact Shimura varieties of type O(p,2) and U(p,1), we show that the resulting local archimedean height pairings are related to special values of derivatives of Siegel Eisentein series. A conj…

Paper bridges matching rules and height functions in aperiodic tilings.

Study the landscape of Lipschitz functions between manifolds using persistent homology.

Study on linking numbers in random book embeddings of complete graphs.

Study on algebraic curves' invariants and vanishing criteria.

Signed heights of knotoids are defined and studied.

Analyzes Gerstner's trochoidal waves and their geometric properties.

Estimates heights of special surfaces in warped products.

Constructs currents and heights on K3 surfaces.

Paper proves unbounded stabilization heights of fiber surfaces using Hopf invariant.

The abstract discusses connections between K-stability, heights, and rational points on Fano varieties.

Computes canonical heights for arithmetic log surfaces using Hurwitz zeta function.

We construct genomic predictors for heritable and extremely complex human quantitative traits (height, heel bone density, and educational attainment) using modern methods in high dimensional statistics (i.e., machine learning). Replication tests show that these predictors capture, respectively, $\sim$40, 20, and 9 perc…

In the following text we prove that for all finite $p\geq0$ there exists a topological graph $X$ such that $\{p,p+1,p+2,\ldots\}\cup\{+\infty\}$ is the collection of all possible heights for transformation groups with phase space $X$. Moreover for all topological graph $X$ with $p$ as height of transformation group $(H…

In this paper, we investigate three geometrical invariants of knots, the height, the trunk and the representativity. First, we give a conterexample for the conjecture which states that the height is additive under connected sum of knots. We also define the minimal height of a knot and give a potential example which has…

The stabilisation height of a fibre surface in the 3-sphere is the minimal number of Hopf plumbing operations needed to attain a stable fibre surface from the initial surface. We show that families of fibre surfaces related by iterated Stallings twists have unbounded stabilisation height.

We study the singularities of the members of the family of height functions on Whitney umbrellas, which is also known as cross-caps, and show that the family of the height functions is a versal unfolding. Moreover, we study local intersections of a Whitney umbrella with a hyperplane through its singular point.

Defines height pairing for differential forms on Riemann surface degenerations.

Study uses satellite and lidar data to map forest height and biomass in France.

Study describes singularities of height functions on specific singular surfaces.

The paper modifies a warped product space to find conditions for constant height functions.

We introduce a new method for detection of long-range cross-correlations and multifractality - multifractal height cross-correlation analysis (MF-HXA) - based on scaling of qth order covariances. MF-HXA is a bivariate generalization of the height-height correlation analysis of Barabasi & Vicsek [Barabasi, A.L., Vicsek,…

Persistent Legendrian contact homology distinguishes knots using height functional.

We describe spaces of essential finite height (measured) laminations in a surface $S$ using a parameter space we call $\mathbb S$, an ordered semi-ring. We show that for every finite height essential lamination $L$ in $S$, there is an action of $π_1(S)$ on an $\mathbb S$-tree dual to the lift of $L$ to the universal co…

We extend the Faltings modular heights of abelian varieties to general arithmetic varieties and show direct relations with the Kahler-Einstein geometry, the Minimal Model Program, heights of Bost and Zhang, and give some applications. Along the way, we propose arithmetic Yau-Tian-Donaldson conjecture, an equivalence of…

This paper exhibits equivalences of 2-stacks between certain models of $\mathbb{S}^1$-gerbes and differential 3-cocycles. We focus primarily on the model of Dixmier-Douady bundles, and provide an equivalence between the 2-stack of Dixmier-Douady bundles and the 2-stack of differential 3-cocycles of height 1, where the …

The paper establishes a relation between knotoid crossing number and height.

We classify, in terms of topology of highest arcs, low height non-simple geodesics on the modular hyperbolic punctured sphere with three elliptic fixed points of order two. Of eight possible types, exactly one consists of geodesics that form a bigon about the cusp; we express all such geodesics in terms of Markoff trip…

We consider height functions on symmetric spaces $M\cong G/K$ embedded in the associated matrix Lie group $G$. In particular we study the relationship between the critical sets of the height function on $G$ and its restriction to $M$. Also we prove that the gradient flow on $M$ can be integrated by means of a generaliz…

New neural network architecture with height adds expressive power.

The height function of various surfaces decomposes into finite sums of scaled and translated versions of itself.

Sharp bounds on K-semistable Fano varieties for low dimensions.

Minimal submanifolds confined in space are highly restricted.

In this paper, we give a height estimate for constant mean curvature graphs. Using this result we prove two results of uniqueness for the Dirichlet problem associated to the constant mean curvature equation on unbounded domains.

New method predicts wave height exceedance probabilities.

Sharp bounds on Fano varieties' heights proven for specific cases.

DeepMIDE forecasts wind speeds across space, time, and height for offshore wind energy.

The paper derives height estimates for surfaces with constant curvature in warped product spaces.

Given a finite graph of relatively hyperbolic groups with its fundamental group relatively hyperbolic and edge groups quasi-isometrically embedded and relatively quasiconvex in vertex groups, we prove that vertex groups are relatively quasiconvex if and only if all the vertex groups have finite relative height in the f…

The paper simplifies arguments for stationary varifolds results.

Study enhances neural network predictions for wave height using topological features.

Let (X,L) be a polarized manifold. Assume that the automorphism group is finite. If the height discrepancy of (X,L) is O(d^2) then (X,L) admits a csck metric in the first chern class of L if and only if (X,L) is asymptotically stable.

In this paper we obtain a sharp height estimate concerning compact hypersurfaces immersed into warped product spaces with some constant higher order mean curvature, and whose boundary is contained into a slice. We apply these results to draw topological conclusions at the end of the paper.

In this paper we obtain height estimates for compact, constant mean curvature vertical graphs in the homogeneous spaces $\mathrm{Nil}_3$ and $\widetilde{PSL}_2(\mathbb{R})$. As a straightforward consequence, we announce a structure-type result for proper graphs defined on relatively compact domains.