Middle East Technical University Department of Mathematics Fall 1999

INTRODUCTION TO TOPOLOGY

OF REAL ALGEBRAIC CURVES

Code: Math 459 (3-0)3

Instructor: Sergey Finashin

Catalog description: Affine and projective real algebraic curves, their complexification; singular points and their bifurcations; intersection of curves and Bezout theorem; the space of curves; Hilbert’s Problem 16

Prerequisite Math 252, Math 262

Textbook:

V.M.Kharlamov, V.A.Rokhlin, O.Ya.Viro, Topological Properties of Real Plane Algebraic Curves (Chap. I-II); (available from the instructor or in the Department Library)

Reference Books: Miles Reid, Undergraduate Algebraic Topology (Chap. 1). Robert J. Walker, Algebraic Curves (Chap. 2–3).

Course Objectives: The aim of this course is to give the students a basic knowledge of topological and algebro-geometric ideas using concrete geometric objects (real algebraic curves). This course may develop a geometric intuition and give the students an idea about a circle of concepts in modern mathematics.