Related papers: Slope Estimates for Generalized Artin-Schreier Cur…

The purpose of this article is to prove a "Newton over Hodge" result for finite characters on curves. Let $X$ be a smooth proper curve over a finite field $\mathbb{F}_q$ of characteristic $p\geq 3$ and let $V \subset X$ be an affine curve.…

We develop the theory of generalized bi-Hamiltonian reduction. Applying this theory to a suitable loop algebra we recover a generalized Drinfeld-Sokolov reduction. This gives a way to construct new examples of algebraic Frobenius manifolds.

We outline a strategy for computing intersection numbers on smooth varieties with torus actions using a residue formula of Bott. As an example, Gromov-Witten numbers of twisted cubic and elliptic quartic curves on some general complete…

We prove an averaging formula for the canonical archimedean height pairing of special divisors with weights over orthogonal and unitary Shimura curves in terms of derivatives of Whittaker functions.

In this paper, we study the Newton polygons for the $L$-functions of $n$-variable generalized Kloosterman sums. Generally, the Newton polygon has a topological lower bound, called the Hodge polygon. In order to determine the Hodge polygon,…

In this paper, we investigate the general notion of the slope for families of curves $f: X \to Y$. The main result is an answer to the above question when $\dim Y = 2$, and we prove a lower bound for this new slope in this case over fields…

In this study, we define some new types of ruled surfaces called slant ruled surfaces. We give some characterizations for a regular ruled surface to be a slant ruled surface in Euclidean 3- space. We show that if the slant ruled surface is…

In this paper, we establish the curvature estimates for a class of Hessian type equations. Some applications are also discussed.

Let $\rho$ be a mod $\ell$ Galois representation. We show how to compute $\rho$, given the characteristic polynomial of the image of the Frobenius at one prime $p$ and a curve $C$ whose Jacobian contains $\rho$ in its $\ell$-torsion. The…

For an elliptic curve A defined over a global function field K of characteristic p>0, the p-Selmer group of the Frobenius twist of A tends to have larger order than that of A. The aim of this note is to discuss this phenomenon.

In this paper, we use the blending functions of Bernstein polynomials with shifted knots for construction of Bezier curves and surfaces. We study the nature of degree elevation and degree reduction for Bezier Bernstein functions with…

In this study, we consider curves of generalized AW(k)-type of Euclidean n-space. We give curvature conditions of these kind of curves.

We present a generalization of Schlick's bias and gain functions -- simple parametric curve-shaped functions for inputs in [0, 1]. Our single function includes both bias and gain as special cases, and is able to describe other smooth and…

The main result of this paper gives a plenary proof on the curvature estimates for $k$ curvature equations with general right hand sides with $n<2k$ based on a concavity inequality. We further give a explicit lower bound of the inequality.

We suggest a modification of the estimate for weighted Sobolev norms of solutions of parabolic equations such that the matrix of the higher order coefficients is included into the weight for the gradient. More precisely, we found the upper…

We prove generalized Virasoro constraints for the relative Gromov-Witten theories of all nonsingular target curves. Descendents of the even cohomology classes are studied first by localization, degeneration, and completed cycle methods.…

This paper describes a class of Artin-Schreier curves, generalizing results of Van der Geer and Van der Vlugt to odd characteristic. The automorphism group of these curves contains a large extraspecial group as a subgroup. Precise knowledge…

We propose a robust method for location estimation in various matrix manifolds based on the projected Frobenius median, which is closely related to the spatial median. This method applies broadly to matrix manifolds, including Stiefel and…

We study the number of rational points of smooth projective curves over finite fields in some relative situations in the spirit of a previous paper from an euclidean point of vue. We prove some kinds of relative Weil bounds, derived from…

We study some kinds of generalizations of Schr\"oder paths below a line with rational slope and derive the $q$-difference equations that are satisfied by their generating functions. As a result, we establish a relation between the…