Complex analysis and algebraic geometry

Complex Analysis and Algebraic Geometry

The theme of these four lectures is roughly "the history of, and some recent developments in, the study of algebraic geometry by analytic methods". Since this topic is much too broad I have chosen to isolate one particular analytic tool, the local notion of residue and subsequent global residue theorem, and will attempt to illustrate some ways in which residues may be used in both classical and...

Reprinted from Complex Analysis and Algebraic Geometry

General Algebraic Geometry and Formal Concept Analysis

This paper describes the interaction between classical Algebraic Geometry, General Algebra, and Formal Concept Analysis. The mathematical foundations of Formal Concept Analysis can be found in ([GW99]). Its goal is to elaborate the general core of the basic results of Algebraic Geometry using this interaction. We start from a general polynomial context of the form Kn,A := (A, Fn(X,A) × Fn(X,A),...

Algebraic Geometry and Computer Vision : Polynomial Systems , Real and Complex

We review the diierent techniques known for doing exact computations on polynomial systems. Some are based on the use of Grr obner bases and linear algebra, others on the more classical resultants and its modern counterparts. Many theoretical examples of the use of these techniques are given. Furthermore, a full set of examples of applications in the domain of artiicial vision, where many const...

Introductory Geometry: Algebraic Geometry