Algebra and Combinatorics Seminar

Date: February 7, 2020

Time: 3:00PM - 3:50PM

Location: BLOC 628

Speaker: Luca Schaffler, University of Massachusetts Amherst

Title: A Pascal's theorem for rational normal curves

Abstract: Pascal's theorem gives a synthetic geometric condition for six points A,...,F in the projective plane to lie on a conic. Namely, that the intersection points of the lines AB and DE, AF and CD, EF and BC are aligned. In higher dimension, one could ask: is there a coordinate-free condition for d+4 points in d-dimensional projective space to lie on a degree d rational normal curve? We find many of these conditions by writing in the Grassmann-Cayley algebra the defining equations of the parameter space of d+4 ordered points that lie on a rational normal curve of degree d. This is joint work with Alessio Caminata.