论文标题
立方体的FANO方案的变形
Deformations of the Fano scheme of a cubic
论文作者
论文摘要
我们研究了Fano方案的变形理论$ \ MATHRM {F} = \ MATHRM {F}（\ Mathrm {X}）$在Cubic $ \ Mathrm {x} $ D $ D $的$ \ Mathrm {X} $上只有一定多个单眼性。通过采用相对的FANO方案，我们定义了形态学$η：\ Mathscr {d} _ {\ Mathrm {x}} \ rightArrow \ MathScr {d} _ {\ Mathrm {f}} $与$ \ m rmm {x} $ {x} $ rm at $ rm {x} $的本地moduli函数我们表明，对于$ d \ geqslant 5 $，$η$产生一阶变形的同构；特别是，每当$ \ mathrm {h}^{0}（θ_ {\ mathrm {x}}}）= 0 $时，$η$是同构的。
We study the deformation theory of the Fano scheme $\mathrm{F}=\mathrm{F}(\mathrm{X})$ of lines on a cubic $\mathrm{X}$ of dimension $d$ with only finitely many singularities. By taking the relative Fano scheme, we define a morphism $η:\mathscr{D}_{\mathrm{X}}\rightarrow\mathscr{D}_{\mathrm{F}}$ of the local moduli functors associated to $\mathrm{X}$ and $\mathrm{F}$, respectively. We show that for $d\geqslant 5$, $η$ yields an isomorphism on first-order deformations; in particular, $η$ is an isomorphism whenever $\mathrm{H}^{0}(Θ_{\mathrm{X}})=0$.
