Instructor: Dr. Andras NEMETHI
Text: your class notes
Reference books:
William Fulton: Algebraic Curves: An Introduction to Algebraic Geometry
Gerd Fischer: Plane Algebraic Curves, AMS, 2001
E. Briekorn, H Knorer: Plane Algebraic Curves, Birkhauser, 2012
R. Shafarevich: Basic Algebraic Geometry 1 and 2, Springer Verlag 1977, 1994.
J. Harris: Algebraic Geometry, A First Course, Graduate Texts in Math.
133, Springer- Verlag New York, 1992
Ph. Griffiths, J. Harris: Principles of Algebraic Geometry, John Wiley
& Sons, Inc., 1978
R. Hartshorne: Algebraic Geometry, Graduate Texts in Math. 52,
Springer-Verlag
Prerequisite: basic group theory, basic ring theory (ideals, modules
over rings, localizations, primary decomposition), field theory, formal
series.
Topics:
- Equations in the affine plane
- Curves in the affine plane
- Curves in the projective plane
- Irreducible decompositions
- The local picture, singular points, local irreducible components
- Bezout's Theorem
- The splitting lemma
- Pappus theorem, Pascal theorem
- Inflection points, Hessian
- smooth cubics, the group law
- divisor on projective curves
- divisor class group
.