Topics in Algebraic Geometry, II

代數幾何專題 (二)

Course Information

Instructor : Jungkai Chen陳榮凱

Place: Old Math Bldg 103

Hours: Tue. 9:10-12:10

First meeting

Feb. 21 (Tue.) 9:10

Syllabus

The two main theme of this course are toric varieties and moduli spaces of curves. There are some important recent developments in algebraic geometry using the geometry of moduli spaces. One of our goal is to study the quautum cohomology constrcucted on the moduli spaces of curves.

Another main theme is toric varieties. Toric varieties provide fruittul concrete examples. It would be nice for students who know some general theory, such as Hartshorne’s book, get their hands dirty by working on toric varieties.

Prerequisite

Any ambitious student is welcome.

The potential speakers are expected to have general background in algebra, topology, complex and algebraic geometry.

Reference:

1. Harris, Joe; Morrison, Ian Moduli of curves. Graduate Texts in Mathematics, 187. Springer-Verlag, New York, 1998.

2. Fulton, William Introduction to toric varieties. Annals of Mathematics Studies, 131. The William H. Roever Lectures in Geometry. Princeton University Press, Princeton, NJ, 1993.

3. Fulton, W.; Pandharipande, R. Notes on stable maps and quantum cohomology. Algebraic geometry---Santa Cruz 1995, 45--96, Proc. Sympos. Pure Math., 62, Part 2, Amer. Math. Soc., Providence, RI, 1997.

4. Oda, Tadao Convex bodies and algebraic geometry. An introduction to the theory of toric varieties. Translated from the Japanese. Ergebnisse der Mathematik und ihrer Grenzgebiete (3) 15. Springer-Verlag, Berlin, 1988.

Grading:

Presentation 50 %

Term paper 50 %