Back to Algebraic Geometry Seminar: Spring 2008
Algebraic Geometry Seminar
Date: Tuesday, Jan 15, 2008
Time: 3:30PM - 4:30PM
Location: LCB 323
3 pm, LCB 225
Dave Anderson
University of Michigan
Title |
Chern class formulas for G 2 degeneracy loci |
Abstract |
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, and it is useful to have formulas for the cohomology classes of such loci in terms of the Chern classes of E, F, and V. Many variations are possible: 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 discuss octonion bundles, and describe the G 2 flag variety in concrete, linear-algebraic terms. |
Algebraic Geometry