Topics in Algebraic Geometry I
Instructor: Jungkai
Alfred Chen
Office: Old
Math. Bldg 108
I.
Contents:
1.
Algebraic Curves and Algebraic Surfaces
a. Divisors, line bundles
b. Riemann-Roch theorem
c. Cohomology theory
d. Intersection theory, Hodge
index theorem
e. Surface singularities
f. Birational maps of surfaces
g. Ruled surfaces
h. Elliptic surfaces
i.
Classification of surfaces
2.
Minimal Model Program
a. Nef, big and ample
Q-divisors
b. Cone theorem
c. Contraction theorem
d. Flips and flops
e. Existence and termination of
flips in dimension 3
f. Terminal singularities in
dimension 3
g. Contraction maps in
dimension 3
h. Some effective results in
dimension 3
II.
Course Goal:We would like introduce
some recent developments in algebraic geometry.
III.
Course prerequisite: Algebra
IV.
Reference material ( textbook(s) ):
a. Kollar, J., Mori, S., Birational Geometry of Algebraic Varieties, Cambridge University Press
b. Beauville , A., Complex Algebraic Surfaces, Cambridge University Press
c. Hacon,C., The minimal model program for log varieties of general type,
http://www.math.utah.edu/~hacon/MMP.pdf
V.
Grading scheme:
a. Term Paper
70%
b. Presentation and
Participation 30%