Math 625, spring 2021
Algebraic Geometry
- Faculty: David Harbater
- E-mail:
harbater AT math.upenn.edu
- Telephone: (215) 898-9594; Department office: (215) 898-8178
- Office: DRL
4E2A; Department office: DRL 4W1-6.
- Office hours: By appointment.
Second semester graduate algebraic geometry.
This course will focus on algebraic curves and surfaces, especially over an algebraically closed field. Topics on curves will include Riemann-Roch, the Riemann-Hurwitz formula, embeddings in projective space, elliptic curves, Jacobians of curves, and related topics. The study of surfaces will include the adjunction and projection formulas, Riemann-Roch for surfaces, Noether's formula, Hodge Index Theorem, Nakai-Moishezon Criterion, ruled surfaces, monoidal transformations, and related topics. The course will also develop and use cohomology for schemes, both from the Cech and derived functor points of view, a key result being Serre Duality. Other types of cohomology in algebraic geometry will also be discussed.
Class schedule: Mon and Wed, 10:30-noon, on Zoom, from Jan. 20 to April 28, 2021.
(No class on Fri., Feb. 12; Wed., March 10; Fri., March 12.)
Main reference:
- "Algebraic Geometry" by Robin Hartshorne. Springer, Graduate Texts in Mathematics, volume 52, 1977. We will focus on Chapters 3-5.
(Available on the Math 625 course site on Canvas, under the tab Course Materials @ Penn Libraries.)
Other useful references:
"The Red Book of Varieties and Schemes" by David Mumford. Springer, Lecture Notes in Mathematics,
volume 1358, 1974 and 1999.
"Principles of Algebraic Geometry" by Phillip Griffiths and Joseph Harris. Wiley, 1978.
There will be regular problem sets. Class participation is expected.
Homework assignments for
Math 625