Determinant of Complexes and Higher Hessians

Abstract. Let X ⊂ Pr be a smooth algebraic curve in projective space, over an algebraically closed field of characteristic zero. For each m ∈ N, the m-flexes of X are defined as the points where the osculating hypersurface of degree m has higher contact than expected, and a hypersurface H ⊂ Pr is called a m-Hessian if it cuts X along its m-flexes. When X is a complete intersection, we give an expression for a (rational) m-Hessian as the determinant of a complex of graded free modules naturally associated to X.