Dave Anderson

Chern class formulas for G_2 degeneracy loci

Let V be a vector bundle of rank n on a variety X, with subbundles E and F of respective ranks e and f. The locus of points of X where the fibers of E and F intersect in dimension more than e+f-n is a basic example of a degeneracy locus. What is a formula for the cohomology class of such a locus, in terms of the Chern classes of E, F, and V? In this simple case, the answer is easy, but many variations are possible: roughly, there should be one for each Lie type, and for each element of the corresponding Weyl group. For classical types, formulas were given by Giambelli-Thom-Porteous, Kempf-Laksov, Harris-Tu, and Fulton. In this talk, I will give formulas corresponding to exceptional type G_2. Along the way, I'll describe the G_2 flag variety in concrete, linear-algebraic terms. (This talk is rated PG-13, for mild non-associative multiplication.)