# Algebraic Geometry I (V4A1)

D. Huybrechts**Classes:**Monday 12:00 ct - 14:00 Uhr, Kleiner Hörsaal Wegelerstr. 10 Friday 14:00 ct - 16:00 Uhr, Grosser Hörsaal Wegelerstr. 10

**Content:**The course introduces the modern language of algebraic geometry: sheaves, schemes, cohomology. The functorial point of view is emphasized. A basic knowledge of commutative algebra (prime ideals etc) is assumed, more advanced material will not be strictly necessary. David Mumford 1975: [Algebraic geometry] 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! In one respect this last point is accurate ...

**References:**R. Hartshorne: Algebraic Geometry GTM 52. Springer. (This is still the most commonly used source.) D. Eisenbud and J. Harris, The Geometry of Schemes, GTM 197, Springer. U. Goertz, T. Wedhorn: Algebraic Geometry I. Vieweg. G. Harder: Lectures on algebraic geometry 2. Vieweg. Q. Liu: Algebraic Geometry and Arithmetic Curves (Oxford Graduate Texts in Mathematics) D. Mumford: The Red book of varieties and schemes. Springer LN 1358. R. Vakil: Foundations of algebraic geometry. Online lectures.

**Tutorials:**- Tue 16-18 Uhr - Seminarraum 0.007 (Galinat). - Wed 16-18 Uhr - Seminarraum 0.008 (Neupert). One of the two (probably Neupert's) will be used to fill gaps in commutative algebra and is recommended for those students who have not followed my class last term.

**Exercises**will be announced here. They are to be handed in directly to the tutors.

Klausur: 13.7., 8-10 am, Kleiner Hörsaal Wegelerstr. 10

Wiederholungspruefung: 31.8.

For further information contact huybrech@...