College of Liberal Arts and Sciences

# Department of Mathematics

## Algebra Seminar

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Title: Equations for point configurations to lie on a rational normal curve
Speaker: Luca Schaffler (Univeriversity of Massachusetts Amherst )
Time: Wednesday, November 14, 2018 at 11:15 am
Place: MONT 313Abstract: Let $V_{d,n}\subseteq(\mathbb{P}^d)^n$ be the Zariski closure of the set of $n$-tuples of points lying on a rational normal curve. The variety $V_{d,n}$ was introduced because it provides interesting birational models of $\overline{M}_{0,n}$: namely, the GIT quotients $V_{d,n}/ /SL_{d+1}$. In this talk our goal is to find the defining equations of $V_{d,n}$. In the case $d=2$ we have a complete answer. For twisted cubics, we use the Gale transform to find equations defining $V_{3,n}$ union the locus of degenerate point configurations. We prove a similar result for $d\geq 4$ and $n=d+4$. This is joint work with Alessio Caminata, Noah Giansiracusa, and Han-Bom Moon.

Organizer: Aurel Mihai Fulger