Abstract: The degree of a projective variety is one of the most important numerical invariants in algebraic geometry. A basic fact for its calculation is Bezout's Theorem, which led to many ingenious computations of the degrees of rank varieties in the 19th century by Cayley, Salmon, Roberts, Cremona, Schubert, Segre, Pieri, and Giambelli. Nowadays we search for formulas for the fundamental classes of degeneracy loci of vector bundle morphisms in terms of the characteristic classes of bundles involved. We shall discuss such formulas of Lascoux, Kempf-Laksov, the speaker, Fulton, Buch-Fulton, and others. Some applications will be presented.

Piotr Pragacz (Polish Academy of Sciences)

General Seminar, 22.04.2004