25/02/2014, 11:15 — 12:15 — Room P3.10, Mathematics Building
Alfonso Zamora, Instituto Superior Tecnico
GIT and symplectic stability(II)
Geometric Invariant Theory (GIT) is a powerful tool to study
quotients of algebraic varieties by the action of Lie groups,
related to symplectic quotients by the Kempf-Ness theorem. From
both points of view a notion of stability for the orbits of the
group action plays a prominent role.
In the lectures we will give the basic notions and ideas behind
GIT stability, symplectic stability and the Kempf-Ness theorem.
We will pay special attention to the unstable orbits for which
one can finds a "maximal way to destabilize" them. This idea can be
seen from both the algebraic and the symplectic point of view and
we will show this coincidence. All the treatment will be done
through three (basic but very illustrative) examples: the obtention
of the projective space as a quotient, the moduli space of
configurations of n points in the projective line (related to the
moduli space of polygons) and the obtention of the grassmanian as a
quotient.