16,051 formulas for Ottaviani's invariant of cubic threefolds

Abstract

We provide explicit combinatorial formulas for Ottaviani's degree 15 invariant which detects cubics in 5 variables that are sums of 7 cubes. Our approach is based on the chromatic properties of certain graphs and relies on computer searches and calculations.

10 pages, 4 figures, 1 ancillary file