论文标题
黑森州地图
The Hessian map
论文作者
论文摘要
在本文中，我们研究了Hessian Map $ h_ {d，r} $，该$将其与$ {\ Mathbb p}^r $ in n ymerface相关联，其Hessian HyseRurface。我们研究了这张地图的一般属性，并证明：$ h_ {d，1} $如果$ d \ geq 5 $;我们详细研究地图$ h_ {3,1} $，$ h_ {4,1} $和$ h_ {3,2} $;我们研究了Hessian Map限制$ d $的高度弯曲面源，而Waring等级$ r+2 $ in $ {\ Mathbb p}^r $，证明该限制是在$ r \ geq 2 $和$ d \ d \ egeq 3 $中的$ r \ geq 2 $ \ geq 2 $和$ d \ geq 3 $的注入，这意味着$ h_^3，3，3,3,3,3,3 ,，我们证明，Hessian地图的差异在$ d $的通用高度上是最大排名，而Waring等级$ r+2 $ in $ {\ MATHBB P}^r $，只要$ r \ r \ geq 2 $ 2 $和$ d \ d \ geq 3 $。
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 $d\geq 5$; 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 $r\geq 2$ and $d\geq 3$, 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 $r\geq 2$ and $d\geq 3$.
