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