The Hessian map

2020/06/12 by Ciliberto, Ciro, Ottaviani, Giorgio · 2 citations
#14E05 #14J70 #14N05 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2006.07213

Abstract

In this paper we study the Hessian map h_d,r which associates to any hypersurface of degree d in \mathbb P^r its Hessian hypersurface. We study general properties of this map and we prove that: h_d,1 is birational onto its image if d≥ 5; we study in detail the maps h_3,1, h_4,1 and h_3,2; we study the restriction of the Hessian map to the locus of hypersurfaces of degree d with Waring rank r+2 in \mathbb P^r, proving that this restriction is injective as soon as r≥ 2 and d≥ 3, which implies that h_3,3 is birational onto its image; we prove that the differential of the Hessian map is of maximal rank on the generic hypersurfaces of degree d with Waring rank r+2 in \mathbb P^r, as soon as r≥ 2 and d≥ 3.

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• Detecting Direct Sums of Tensors and Their Limits
• The Hesse Pencil Variety

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