# An asymptotic Mukai model of M_6

## 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.

Tuesday, April 9th, at 4:00pm in HBH 227

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