Algebraic Geometry 2 (Schemes and Cohomology), Summer 2010

Prof. Dr. Gavril Farkas
e-mail: farkas@math.hu-berlin.de

" As it turned out, the field seems to have acquired the reputation of being esoteric, exclusive and very abstract with adherents who are secretly plotting to take over all the rest of mathematics!'' (David Mumford, 1975)

"...algebraic geometry was the only part of mathematics where a counterexample to a theorem was considered a beautiful addition to it" (Paul Halmos, "I want to be a mathematician" 1985)

This is the webpage of the couse Algebraic Geometry 2, being taught at the Humboldt University in Berlin, in the Summer Semester 2010. The class meets Mo 13:15-15:00 in RUD 25 1.115 and on Di 9:15-11 in RUD 25 Raum 3.008. The exercise sessions take place Mo 15:15-17 in RUD 25 4.007.

Algebraic geometry occupies a central role in modern mathematics interacting with fields like theoretical physics, number theory, topology and differential geometry. Startling advances in the study of parameter (moduli) spaces have been inspired by ideas from physics, elliptic curves play a crucial role in arithmetic, while the study of real 4-manifolds is very much connected to the classical theory of algebraic surfaces. Within algebraic geometry, there has been great progress over the last three decades especially in the study of classification of varieties of dimension three or more (Minimal Model Program) and the understanding of moduli spaces.
The course deals with schemes and cohomology, the language of modern algebraic geometry.
References:

  • R. Hartshorne, Algebraic Geometry, Springer GTM

  • D. Mumford, The Red Book of Varieties and Schemes, Springer LNM

  • D. Eisenbud and J. Harris, The geometry of schemes, Springer GTM

  • J. Harris, Algebraic Geometry: A first course, Springer GTM


    Exercises:

    Problem set nr. 1
    Problem set nr. 2
    Problem set nr. 3
    Problem set nr. 4