MATH 643 -- Algebraic Geometry

Fall 2006

Instructor: Katia Consani
Office: 216 Krieger Hall
Phone: (410) 516-5116.
Email: [email protected]

Class Times: MTW, 12:00-12:50 pm.
Room: Maryland 217 (first class: Tuesday September 12).

References: There are no required textbooks for the course, but the following references may be useful.

Y. Andre, Une introduction aux motifs, Panoramas et Synteses, 17. Societe Mathematique de France, 2004.

D. Eisembud, Commutative Algebra with a view toward Algebraic Geometry, Springer, 1999.

W. Fulton, Algebraic Curves , Addison-Wesley, 1989.

J. Harris, Algebraic Geometry: a First Course , Springer, 1992.

R. Godement, Topologie algebrique et theorie des fascieaux .

P. Griffiths, J. Harris, Principles of Algebraic Geometry , 1994.

R. Hartshorne, Algebraic Geometry , Springer, 1977.

M. Kashiwara, P. Schapira, Sheaves on Manifolds , Grundlehren der math. Wissenschaften, 292 (1990). ISBN 3540518614 or 0387518614.

Y. Manin, Correspondences, motifs and monoidal transformations.

J. Murre, Lectures on Motives in Transcendental Aspects of Algebraic Cycles: Proceedings of the Grenoble Summer School, 2001 (London Mathematical Society Lecture Note S.).

C. Weibel, An introduction to homological algebra , Cambridge studies in Adv. Math. 38.

Outline of the course: This is an introductory course in algebraic geometry in which students are introduced to the fundamental classic concepts of algebraic geometry such as Zariski topology, affine and projective varieties, some concepts of sheaf and scheme theory through explicit computations and examples and at the same time they also get acquainted with some of the modern aspects of this theory, via the development of suitably chosen topics that are usually explained in the second part of the course. The topic chosen this year will focus on the theory of algebraic correspondences and pure motives and it will be supported by important examples and computations.

Prerequisites: Basic point-set topology and some comfort with manifolds are probably essential. Also useful: some previous exposure to concepts of homological algebra and to the basic notions in ring theory and complex analysis.

Grading: Some exercises will be assigned regularly during lectures. The exercises will not be collected, and in fact there will be no written work required in this course. The final grade will be determined from two components: 1) class participation (i.e. did you basically attend all the lectures and try to ask questions now and then), and 2) a 15-minute oral exam that will be scheduled during the last two or three weeks of the course. During the oral exam you will be expected to explain to me 2 or 3 topics from a list of things we covered during the lectures. The list of possible topics will be determined later. You will know ahead of time exactly which topics you need to present to me, but you may or may not be allowed to choose the topics yourself (I haven't decided yet). Details will be announced later in the course.

Important Note: First class on Tuesday September 12.