Course

M456 - Algebraic Geometry

Course No: 
M456
Credit: 
4
Prerequisites: 
M205
Approval: 
2014
UG-Elective
Syllabus: 
Prime ideals and primary decompositions, Ideals in polynomial rings, Hilbert Basis theorem, Noether normalisation lemma, Hilbert’s Nullstellensatz, Affine and Projective varieties, Zariski Topology, Rational functions and morphisms, Elementary dimension theory, Smoothness, Curves, Divisors on curves, Bezout’s theorem, Riemann-Roch for curves, Line bundles on Projective spaces.
Reference Books: 
  1. J. Harris, “Algebraic geometry”, Graduate Texts in Mathematics 133, Springer-Verlag, 1995.
  2. M. Reid, “Undergraduate Algebraic Geometry”, London Mathematical Society Student Texts 12, Cambridge University Press, 1988.
  3. K. E. Smith et. al., “An Invitation to Algebraic Geometry”, Universitext, Springer-Verlag, 2000.
  4. K. Hulek, “Elementary Algebraic Geometry”, Student Mathematical Library 20, American Mathematical Society, 2003.
  5. I. R. Shafarevich, “Basic Algebraic Geometry 1: Varieties in Projective Space”, Springer, 2013.
  6. R. Hartshorne, “Algebraic Geometry”, Graduate Texts in Mathematics 52, Springer-Verlag, 1977.

Contact us

School of Mathematical Sciences

NISERPO- Bhimpur-PadanpurVia- Jatni, District- Khurda, Odisha, India, PIN- 752050

Tel: +91-674-249-4081

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