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Phillip A. Griffiths, Introduction to Algebraic Curves,
Translations of Mathematical Monographs, 76.
American Mathematical Society, Providence, RI, 1989. x+221 pp.
ISBN: 0-8218-4530-6
Monday |
Riemann surfaces, genus, Euler
characteristic, meromorphic functions, multiplicity of a
function at a point, ramification index, differentials,
Stokes' theorem, residues of differentials,
Poincare-Hopf formula |
Tuesday |
Projective space, algebraic varieties,
divisors, degree, tangent spaces, holomorphic maps from
Riemann surfaces to projective spaces |
Wednesday |
Local structure of algebraic curves,
intersection numbers, Bezout's theorem, Riemann-Hurwitz
theorem, the degree-genus formula |
Thursday |
Day off |
Friday |
The Riemann-Roch theorem, applications to
g=0 and g=1 cases, canonical mapHyperelliptic and
non-hyperelliptic curves, g=2, g=3 and g=4 cases |
Saturday |
Hyperelliptic and non-hyperelliptic curves, g=2, g=3 and g=4 cases |
Sunday |
Abel's theorem, Jacobi inversion, Torelli
theorem, J-invariant and the biholomorphic
classification of elliptic curves |