An asymptotic Mukai model of M6
Evgeny Mayanskiy, Penn State
We will present a solution to the GIT problem coming from the Mukai
construction of genus 6 curves as complete intersections of the Grassmannian
G(2,5) of lines in P4 (in the Pl\"ucker embedding) and a 4-dimensional quadric.
In particular, we will describe explicitly curves parameterized by the
'asymptotic' GIT quotient (i.e. when our vGIT parameter t-> \infty). The same
space was studied (entirely independently) in the very recent paper by Fabian
M\"uller
Along the way we will use Ozeki classification of orbits of a certain
prehomogeneous vector space in order to complement some earlier (from 1930)
results of J.A. Todd on linear complexes of lines in P4.
Our work is a part of a larger project joint with Damiano Fulghesu.