University of Regina
Department of Mathematics and Statistics
Speaker: D.Z. Djokovic (University of Waterloo)
Title: On the Geometry of Unimodular Equivalence Classes of Bilinear
Date: Friday, March 5, 2004
Place: Math & Stats Lounge (CW 307.18)
Let V be an n-dimensional vector space over an algebraically closed
field K of characteristic 0 and consider the natural action of SLn on B, the
space of bilinear forms f : V × V K. Denote by B//SLn the categorical
quotient, which is known to be an affine space of dimension m + 1 (where
n = 2m or 2m + 1). We study the canonical projection : B B//SLn
and its fibers -1((f)), f B. The zero fiber, also known as the null-cone,
N = -1((0)) plays a special role.
The following questions will be answered in full:
1) Is N the union of only finitely many SLn-orbits?
2) Characterize the closed SLn-orbits.