Math 507A and 508A
Algebraic Geometry
Sándor Kovács(Autumn 2005), Paul Smith (Winter 2006)
Autumn 2005 (M/W/F 9:30) and Winter 2006, (M/W/F/ 2:30)
Two-quarter sequence covering the basic theory of affine and projective
varieties, rings of functions, the Hilbert Nullstellensatz, localization,
and dimension; the theory of algebraic curves, divisors, cohomology, genus,
and the Riemann-Roch theorem; and related topics. Prerequisite: MATH 506.
The first quarter will begin with an introduction to algebraic
geometry. Topics include affine and projective varieties, Zariski topology,
Hilbert Nullstellensatz, regular and rational maps, blowing up, resolution
of singularities of curves, basic intersection theory, Bezout's theorem.
Prerequisites Math 504/505/506 or equivalent.