相关论文: Studying the multivariable Alexander polynomial by…

We prove a generic Torelli theorem for Jacobian elliptic surfaces, provided that the geometric genus is large compared to the irregularity. The result is effective to the extent that defining equations for the base curve are recovered from…

This paper is the first in a series of three devoted to the smooth classification of simply connected elliptic surfaces. The method is to compute some coefficients of Donaldson polynomials of $SO(3)$ invariants whose second Stiefel-Whitney…

We study the structure of collections of algebraic curves in three dimensions that have many curve-curve incidences. In particular, let $k$ be a field and let $\mathcal{L}$ be a collection of $n$ space curves in $k^3$, with…

The classical polynomial interpolation problem in several variables can be generalized to the case of points with greater multiplicities. What is known, as yet, is essentially concentrated in the Alexander-Hirschowitz Theorem which says…

In this paper we develop an abstract theory for the Codazzi equation on surfaces, and use it as an analytic tool to derive new global results for surfaces in the space forms ${\bb R}^3$, ${\bb S}^3$ and ${\bb H}^3$. We give essentially…

In this paper we refine the main result of a previous paper of the author with Grimeland on derived invariants of surface algebras. We restrict to the case where the surface is a torus with one boundary component and give an easily…

The purpose of this paper is: 1) to explain the Seiberg-Witten invariants, 2) to show that - on a K\"ahler surface - the solutions of the monopole equations can be interpreted as algebraic objects, namely effective divisors, 3) to give - as…

We give a new construction of the one-variable Alexander polynomial of an oriented knot or link, and show that it generalizes to a vector valued invariant of oriented tangles.

We study the rational approximation properties of special manifolds defined by a set of polynomials with rational coefficients. Mostly we will assume the case of all polynomials to depend on only one variable. In this case the manifold can…

We describe a multivariable polynomial invariant for certain class of non isolated hypersurface singularities generalizing the characteristic polynomial on monodromy. The starting point is an extension of a theorem due to Le Dung Trang and…

Here the polynomial interpolation approach is used to introduce the main results on multivariate normal algebraic systems. Next we bring a construction which shows that any standard algebraic system, with finite set of solutions, can be…

In this article, we generalize several fundamental results for arithmetic divisors, such as the continuity of the volume function, the generalized Hodge index theorem, Fujita's approximation theorem for arithmetic divisors and Zariski…

This is the first paper in a series of eight where in the first three we develop a systematic approach to the geometric algebras of multivectors and extensors, followed by five papers where those algebraic concepts are used in a novel…

We prove that two general Enriques surfaces defined over an algebraically closed field of characteristic different from $2$ are isomorphic if their Kuznetsov components are equivalent. We apply the same techniques to give a new simple proof…

To a complex polynomial function $f$ with arbitrary singularities we associate the number of Morse points in a general linear Morsification $f_{t} := f - t\ell$. We produce computable algebraic formulas in terms of invariants of $f$ for the…

We use the square peg problem for smooth curves to prove a generalized table Theorem for real valued functions on Riemannian surfaces with odd Euler characteristic. We then use this result to prove the table conjecture for even functions on…

In this paper, we establish more identities of generalized multi poly-Euler polynomials with three parameters and obtain a kind of symmetrized generalization of the polynomials. Moreover, generalized multi poly-Bernoulli polynomials are…

Multivariable generalizations of the classical Hermite, Laguerre and Jacobi polynomials occur as the polynomial part of the eigenfunctions of certain Schr\"odinger operators for Calogero-Sutherland-type quantum systems. For the generalized…

The aim of this paper is to prove a uniform Fourier restriction estimate for certain $2-$dimensional surfaces in $\mathbb R^{2n}$. These surfaces are the image of complex polynomial curves $\gamma(z) = (p_1(z), \dots, p_n(z))$, equipped…

Let $\mathbb{F}$ be a division ring. In this paper, we extent some of the main well-known results about the resultant of two univariate polynomials to the more general context of an Ore extension $\mathbb{F}[x;\sigma,\delta]$. Finally, some…