相关论文: Real algebraic structures

The paper studies the structure of restricted Leibniz algebras. More specifically speaking, we first give the equivalent definition of restricted Leibniz algebras, which is by far more tractable than that of a restricted Leibniz algebras in…

Chapters 1 to 4 are the lecture notes of my course "Real Algebraic Geometry I" from the winter term 2020/2021. Chapters 5 to 8 are the lecture notes of its continuation "Real Algebraic Geometry II" from the summer term 2021. Chapters 9 and…

We study geometric structures arising from Hermitian forms on linear spaces over real algebras beyond the division ones. Our focus is on the dual numbers, the split-complex numbers, and the split-quaternions. The corresponding geometric…

This paper is a survey on arc spaces, a recent topic in algebraic geometry and singularity theory. The geometry of the arc space of an algebraic variety yields several new geometric invariants and brings new light to some classical…

This short survey article reviews current understand- ing of the structure of noetherian Hopf algebras. The focus is on homological properties. A number of open problems are listed.

In this article we study the transitivity of the group of automorphisms of real algebraic surfaces. We characterize real algebraic surfaces with very transitive automorphism groups. We give applications to the classification of real…

These notes outline some basic notions of Tropical Geometry and survey some of its applications for problems in classical (real and complex) geometry. To appear in the Proceedings of the Madrid ICM.

In this paper we prove the topological uniqueness of maximal arrangements of a real plane algebraic curve with respect to three lines. More generally, we prove the topological uniqueness of a maximally arranged algebraic curve on a real…

Lecture notes of an algebraic geometry graduate course. The topics covered are as follows. Cohomology: ext sheaves and groups, cohomology with support, local cohomology, local duality. Duality: relative duality, Cohen-Macaulay schemes.…

In this thesis we explore natural procedures through which topological structure can be constructed from specific semigroups. We will do this in two ways: 1) we equip the semigroup object itself with a topological structure, and 2) we find…

The geometric algebra is constructed from minimal raw materials.

A general framework for obtaining certain types of contracted and centrally extended algebras is presented. The whole process relies on the existence of quadratic algebras, which appear in the context of boundary integrable models.

This is the first of a series of papers studying real algebraic threefolds using the minimal model program. The main results are outlined in Part II. The present part I. contains the necessary preliminary work concerning terminal…

The aim of these notes is to present an accessible overview of some topics in classical algebraic geometry which have applications to aspects of discrete integrable systems. Precisely, we focus on surface theory on the algebraic geometry…

A uniform space is a topological space together with some additional structure which allows one to make sense of uniform properties such as completeness or uniform convergence. Motivated by previous work of J. Rivera-Letelier, we give a new…

These are extended notes of a course given at Tulane University for the 2015 Clifford Lectures. Their aim is to present structure results for group schemes of finite type over a field, with applications to Picard varieties and automorphism…

The canonical projections of the unit spheres are generalized to special generic maps and round fold maps, for example. They are generalizations from the viewpoint of singularity theory of differentiable maps and these maps restrict the…

This is a short survey on the recent developments made in the integration theory with effective formulas of algebraic structures stronger or higher than Lie algebras.

Rationally convex topological embeddings of compact surfaces (closed or with boundary) into $\mathbb{C}^2$ are constructed.

We conjecture the existence of a simple geometric structure underlying questions of reducibility of parabolically induced representations of reductive p-adic groups.