Seminar

The ring of invariants for the action of the automorphism group of the projective line on the n-fold product of the projective line is a classical object of study. The generators of this ring were determined by Kempe in the 19th century. However, the ideal of relations has been only understood recently in work of Howard, Millson, Snowden and Vakil. They prove that for
n>6, the ideal of relations is generated by quadratic equations using a
degeneration to a toric variety.

I will report on joint work with Benjamin Howard where we compute the Hilbert functions of these rings of invariants, and further study the toric varieties arising in this degeneration. As an application we show that the second Veronese subring of the ring of invariants admits a presentation whose ideal admits a quadratic Gröbner basis.