Mathematics W4045. Algebraic Curves, Spring 2011

Tentative Syllabus

• Affine and projective plane curves
• Riemann surfaces
• Functions on Riemann surfaces
• Maps between Riemann surfaces
• Hurwitz's formula
• The genus of a projective plane curve
• Forms and integration on Riemann surfaces
• Divisors and linear systems
• Bezout's theorem
• Riemann-Roch theorem
• Abel's theorem