Determinant of complexes and higher Hessians

1996/01/02 by Fernando Cukierman, Cukierman, Fernando
Mathematics · #14N99 (Primary) 14M12 (Secondary) #Algebraic Geometry (math.AG) #FOS: Mathematics #alg-geom #math.AG #msc:14M12 #msc:14N99

paper · pdf · doi:10.48550/arxiv.alg-geom/9601001

AMSTeX preprint style

arxiv created 1996/01/02 · arxiv updated 2009/11/30

Abstract

Let X ⊂ \Bbb P^r be a smooth algebraic curve in projective space, over an algebraically closed field of characteristic zero. For each m ∈ \Bbb 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 ⊂ \Bbb P^r 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 Div (in the sense of Grothendieck-Knudsen-Mumford) of a complex of graded free modules naturally associated to X. The construction of this complex involves relating sheaves of differential operators on a scheme and a subscheme, and higher Euler sequences on projective space.

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