Related papers: Height functions associated with closed subschemes

For a smooth, projective complex variety, we introduce several mixed Hodge structures associated to higher algebraic cycles. Most notably, we introduce a mixed Hodge structure for a pair of higher cycles which are in the refined normalized…

Set-functions appear in many areas of computer science and applied mathematics, such as machine learning, computer vision, operations research or electrical networks. Among these set-functions, submodular functions play an important role,…

Using Singular Rescaling We Prove Some Bifurcation Results. This note Presents short proofs for some Bifurcation results which had been appeared with other authors.

The present paper aims to survey known results and to point out the wealth of rather important open problems that are out there.

Here we describe the distribution of rational points on the Hilbert scheme of two points in the projective plane. More specifically, we explicitly describe a two-parameter family of height functions $H_{s, t}$, such that the height function…

It is well-known that every convex function admits an affine support at every interior point of a domain. Convex functions of higher order (precisely of an odd order) have a similar property: they are supported by the polynomials of degree…

In this paper, we propose a new height function for a variety defined over a finitely generated field over Q. For this height function, we will prove Northcott's theorem and Bogomolov's conjecture, so that we can recover the original…

A perspective function is a construction which combines a base function defined on a given space with a nonlinear scaling function defined on another space and which yields a lower semicontinuous convex function on the product space. Since…

In this paper we consider the open complement U of a hypersurface Y=V(a) in an affine scheme X. We study the relations between the affineness of U, the intersection of Y with closed subschemes, the property that every closed surface in U is…

In this paper, we obtain some new results on closed subschemes. Specially, we define natural addition and multiplication on the closed subschemes of a scheme. It is shown that "the multiplication" precisely coincides with the well known…

Estimates of some integrals related to variations of smooth functions are presented.

In this note, we establish some new results on some special types of function algebras and also give new proofs to some existing ones

We give a mathematical structure on an arithmetic surface, that has algebraic meanings over finite places and can estimate the canonical norm for a relative differential form on the arithmetic surface. This will give a lower bound for the…

The present article reveals important properties of the confluent Heun's functions. We derive a set of novel relations for confluent Heun's functions and their derivatives of arbitrary order. Specific new subclasses of confluent Heun's…

This is an informal summary of the main concepts in arXiv:0905.4044, based on notes of various seminars. It gives constructions of higher and derived stacks without recourse to the extensive theory developed by Toen, Vezzosi and Lurie.…

It is known for linear operators with polynomial coefficients annihilating a given D-finite function that there is a trade-off between order and degree. Raising the order may give room for lowering the degree. The relationship between order…

General theory of elliptic hypergeometric series and integrals is outlined. Main attention is paid to the examples obeying properties of the "classical" special functions. In particular, an elliptic analogue of the Gauss hypergeometric…

The height of a knotoid is a measure of how far it is from being a knot. Here we define the positive and negative parts of the height, and we prove that they determine the unsigned height. Some polynomial invariants provide lower bounds for…

In this work, we introduce a new class of non-convex functions, called implicit concave functions, which are compositions of a concave function with a continuously differentiable mapping. We analyze the properties of their minimization by…

The main aim of the present note is to prove new Hadamard like integral inequalities for the product of the convex functions.