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INDIAN INSTITUTE OF SCIENCE
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MA 308: Basic Algebraic Geometry
Credits: 3:0
Prerequisite courses: Algebra II (MA 213).
Pre-requisites :
The course will assume that that the student is comfortable with Abstract Algebra at the level of Galois theory.
We will develop all the Commutative algebra that we will need.
The material to be covered will include:
Affine algebraic sets: Zariski topology, irreducible components, Hilbert Nullstellensatz theorem, maps of algebraic sets
Algebraic varieties: Definitions, affine algebraic varieties, projective varieties, morphisms
Rational functions and rational maps
Algebraic curves, B´ezout’s theorem * Reimann-Roch theorem
Suggested books and references:
William D. Fulton,
Algebraic curves
, available free (and legally) at http://www.math.lsa.umich.edu/ wfulton/CurveBook.pdf.
All Courses
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:
+91 (80) 2293 2711, +91 (80) 2293 2265 ;
E-mail:
chair.math[at]iisc[dot]ac[dot]in
Last updated: 18 Sep 2020