Given a vector bundle on a smooth projective algebraic variety there exists a unique flag of subbundles (the Harder-Narasimhan filtration). In a paper from 1977, S.S. Shatz associated a polygon to this flag of subbundles and named the polygon the Harder-Narasimhan polygon of the vector bundle. In this talk we will present the bits of combinatorics associated with these polygons. This is joint work with A. Dhillon.
Probability and Combinatorics
Thursday, March 1, 2007 - 4:00pm
Mahir Can
University of Western Ontario