The moduli space of points on the projective line and quadratic Groebner bases

Series: 
Algebra Seminar
Monday, December 5, 2011 - 16:05
1 hour (actually 50 minutes)
Location: 
Skiles 006
,  
University of Connecticut
Organizer: 
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 very recently in work of Howard, Millson, Snowden and Vakil. They prove that the ideal of relations is generated byquadratic equations using a degeneration to a toric variety. I will report on joint work with Benjamin Howard where we 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 Groebner basis.