
School of Mathematics and Statistics
Frances Kirwan
Oxford University
Geometric invariant theory and filtrations on bundles
over curves.
Friday 23rd February, 121pm,
Carslaw 159.
To a linear action of a complex reductive group G on
a projective variety X, geometric invariant theory
associates two open subsets of X, whose
elements are respectively the
stable and semistable points for the action, and a
projective variety X//G with a Ginvariant surjective
morphism from the set of semistable points to X//G,
whose restriction to the set of stable points identifies
an open subset of X//G with the orbit space X^{s}/G.
Moduli spaces in algebraic geometry can often be
constructed as such orbit spaces.
Also associated to the linear action, there
is a canonical Ginvariant stratification of X
with the set of semistable points as its open stratum.
In the construction of moduli spaces of bundles
over curves this stratification is given by classifying
bundles according to the type of their HarderNarasimhan
filtrations. The aim of this talk is to discuss some
refinements of this stratification with X^{s} as the open
stratum, and associated refinements of the
HarderNarasimhan filtration of a bundle over a
curve.
