MA 314: Introduction to Algebraic Geometry

Credits: 3:0


Affine algebraic sets, Hilbert basis theorem, Hilbert Nullstellensatz, function field, plane curves, Bezout’s theorem, product, normality, morohisms, Noether normalisation, Graded rings, projective varieties, rational functions, tangent spaces, non- singularity, blowing up points, Riemann-Roch for curves. Schemes examples.


Suggested books :

  1. Shafarevich, I.R., Basic Algebraic Geometry 1, 2nd edition ,Springer-Verlag, 1994.
  2. Smith, K., Kahanpaa, L., Kekalainen, P., Traves, W., An Invitation to Algebraic Geometry ,Springer-Verlag, 2000.
  3. Reid, M., Undergraduate Algebraic Geometry ,London Mathematical Society Student Texts 12, Cambridge University Press, 1988.
  4. Fulton, W., Algebraic Curves (http://math.lsa.umich.edu/CurveBook.pdf) .
  5. Holme, A., A Royal Road to Algebraic Geometry ,Springer,2012.

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Contact: +91 (80) 2293 2711, +91 (80) 2293 2625
E-mail: chairman.math[at]iisc[dot]ac[dot]in