A Beginner's Introduction to Algebraic Geometry

Introduction to Algebraic Geometry


Sudhir R. Ghorpade

Department of Mathematics
Indian Institute of Technology, Bombay
Powai, Mumbai 400076 India
E-mail: srg@math.iitb.ac.in

Version 1.1, October 2007


These notes are based on the single lecture given first in the Science Special Lecture Series of the Karnataka Academy of Science and Technology at the University of Mysore on March 5, 2007, and later during the Short Term Training Programme on Advances in Control Theory at VJTI, Mumbai. The aim has always been to give the participants, who generally had no prior exposure to algebraic geometry, a feeling for the subject and to relate it to topics they may have been familiar with.


1 Preamble 3
2 Theory of Equations 3
3 Analytic Geometry 9
4 Affine Varieties and Hilbert's Nullstellensatz 12
5 Projective Varieties and Bezout's Theorem 14
6 Epilogue 18
References 19

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