Geometry of Quadratic Equations

Lecture Announcement

Module Description (MA5221)

John von Neumann Visiting Professorship

This lecture is held by Prof. Dr. Igor Dolgachev as TUM von Neumann Visiting Professor

Place and time

1. Monday, October 17, 10:15 - 11:45 in MI 00.07.014
2. Friday, October 21, 14:15 - 15:45 in MI 02.06.011
3. Monday, October 24, 10:15 - 11:45 in MI 03.08.011
4. Monday, October 31, 10:15 - 11:45 in MI 03.08.011
5. Monday, November 7, 10:15 - 11:45 in MI 03.08.011
6. Friday, November 11, 14:15 - 15:45 in MI 02.06.011
7. Monday, November 14, 10:15 - 11:45 in MI 03.08.011
8. Friday, November 18, 14:15 - 15:45 in MI 02.06.011
9. Monday, November 21, 10:15 - 11:45 in MI 03.08.011
10. Monday, November 28, 10:15 - 11:45 in MI 03.08.011
11. Monday, December 5, 10:15 - 11:45 in MI 03.08.011
12. Monday, December 12, 10:15 - 11:45 in MI 03.08.011

Abstract

The lecture course consists of 12 lectures and will be devoted to the geometry of projective algebraic varieties defined by quadratic homogeneous equations and linear systems of quadrics. The goal is to cover the following topics:

1. Linear systems of quadrics and their attributes: the base loci, the discriminant varieties, the Jacobian and the Reye varieties.
2. Regular linear systems of quadrics and smooth complete intersections of quadrics.
3. Examples from classical algebraic geometry: quartic del Pezzo surfaces, Kummer surfaces, Cayley symmetroids, Reye congruences of lines.
4. Symmetric determinantal representations of hypersurfaces.
5. Conic and quadric fibrations:relationship with the problems of rationality of algebraic varieties.

Literature

Lecture notes can be found on moodle.

Prerequisites

The main prerequisite for the course will be the familiarity with the basics of algebraic geometry.