Algebraic Geometry 3

In this course we will study the particular class of algebraic varieties known as "abelian varieties. Abelian varieties play a special role in algebraic geoemtry, as they have enough structure to make concrete computations (line bundles, cohomology) possible, but are complicated enough to exhibit a number of very interesting properites. Besides this, one has via the Jacobian varieties a close connection with the geometry of algebraic curves. As text we will mainly use the book of David Mumford, "Abelian Varieties" but will also use Mumford's "Curves and their Jacobians" as well as the book of Swinnerton-Dyer "Analytic theory of abelian varieties". Participants should have already taken algebraic geometry 1 and 2 or equivalents.

 

Texts

Mumford, David, Abelian varieties. Tata Institute of Fundamental Research Studies in Mathematics, No. 5 Published for the Tata Institute of Fundamental Research, Bombay; Oxford University Press, London 1970 viii+242 pp.

Mumford, David, Curves and their Jacobians. The University of Michigan Press, Ann Arbor, Mich., 1975. vi+104 pp.

Swinnerton-Dyer, H. P. F., Analytic theory of abelian varieties. London Mathematical Society Lecture Note Series, No. 14. Cambridge University Press, London-New York, 1974. viii+90 pp.