Some Taylor varieties with null Hessian

Abstract

Taylor varieties ${\mathcal{T}}_{d,e,m}^n$ arise from Taylor expansion of rational functions in $n$ variables. Among them, we look for non-defective hypersurfaces. We prove that the cases $n=2$ and $m=d+2$ give new examples of hypersurfaces with identically null Hessian.

11 pages