相关论文: Jet spaces in complex analytic geometry: an exposi…

This article gives an introduction for mathematicians interested in numerical computations in algebraic geometry and number theory to some recent progress in algorithmic number theory, emphasising the key role of approximate computations…

This article is an introduction to newly discovered relations between volumes of moduli spaces of Riemann surfaces or super Riemann surfaces, simple models of gravity or supergravity in two dimensions, and random matrix ensembles. (The…

In this paper, we present a constructive generalization of metric and uniform spaces by introducing a new class of spaces, called cover spaces. These spaces form a topological concrete category with a full reflective subcategory of complete…

We define and analyze various generalizations of the punctual Hilbert scheme of the plane, associated to complex or real Lie algebras. Out of these, we construct new geometric structures on surfaces whose moduli spaces share multiple…

This paper provides details of the construction, properties and some applications of the ambient metric associated to a conformal class of metrics on a smooth manifold. Existence and uniqueness of formal expansions defining such metrics are…

This is a survey article for the mathematical theory of Witten's Gauged Linear Sigma Model, as developed recently by the authors. Instead of developing the theory in the most general setting, in this paper we focus on the description of the…

In this paper I survey some recent results on finite determination, convergence, and approximation of formal mappings between real submanifolds in complex spaces. A number of conjectures are also given.

This is (raw) lecture notes of the course read on 6th European intensive course on Complex Analysis (Coimbra, Portugal) in 2000. Our purpose is to describe a general framework for generalizations of the complex analysis. As a consequence a…

A short explanation of the complexity of the structure of Demailly-semple invariant jet differentials was given

In this text we expose basic cases of some fundamental ideas and methods of topology. Namely, of homotopy, degree, fundamental group, covering, Whitehead invariant, etc. This is done by considering the elementary example: closed polygonal…

These notes give an elementary approach to parts of the theory of standard Borel and analytic spaces.

The aim of this text is to provide a linguistically accessible, but comprehensive introduction into a variety of topics in dynamical systems and its applications. Whilst preliminary knowledge of dynamical systems is useful, it is not…

The type of a complex projective plane curve has been recently introduced by T. Abe, P. Pokora and the first author. In the same paper they have studied the type two curves. In this paper we study plane curves of type three, with special…

The aim of this paper is to study the Mannheim partner curves in three dimensional Galilean space . Some well known theorems are obtained related to Mannheim curves.

In this paper we study the moduli space of 4-dimensional complex associative algebras. We use extensions to compute the moduli space, and then give a decomposition of this moduli space into strata consisting of complex projective orbifolds,…

In this informal expository note, we quickly introduce and survey compactifications of strata of holomorphic 1-forms on Riemann surfaces, i.e. spaces of translation surfaces. In the last decade, several of these have been constructed,…

An algebraic technique adapted to the problems of the fundamental theoretical physics is presented. The exposition is an elaboration and an extension of the methods proposed in previous works by the aut

New types of designs called nested space-filling designs have been proposed for conducting multiple computer experiments with different levels of accuracy. In this article, we develop several approaches to constructing such designs. The…

We are interested in the local extrinsic geometry of smooth surfaces in 4-space, and classify jets of Monge forms by projective transformations according to $\mathcal{A}^3$-types of their central projections.

Fake projective planes are smooth complex surfaces of general type with Betti numbers equal to those of the usual projective plane. They come in complex conjugate pairs and have been classified as quotients of the two-dimensional ball by…