论文标题
Fano Hypersurfaces上曲线的插值
Interpolation of curves on Fano hypersurfaces
论文作者
论文摘要
在$ \ mathbb p^n $或$ \ mathbb p^n $本身的一般超出表面上，我们证明了任何属的曲线存在，并且取决于经过预期数字$ t $ t $ t $ t $ t $ t $ t $ t $ t $ t $ t $ t $ t $ t $的一般积分或事件的属性的高度。在某些情况下，我们还表明，通过$ t $固定点的曲线家族具有Moduli将军为$ t $点的曲线家族。这些结果暗示着稳定地图的Kontsevich空间上某些相交数量的积极性。 M. C. Chang descib的算术附录将我们的结果适用的数值字符集（$ n，d $，曲线，属，属）。
On a general hypersurface of degree $d\leq n$ in $\mathbb P^n$ or $\mathbb P^n$ itself, we prove the existence of curves of any genus and high enough degree depending on the genus passing through the expected number $t$ of general points or incident to a general collection of subvarieties of suitable codimensions. In some cases we also show that the family of curves through $t$ fixed points has general moduli as family of $t$-pointed curves. These results imply positivity of certain intersection numbers on Kontsevich spaces of stable maps. An arithmetical appendix by M. C. Chang descibes the set of numerical characters ($n, d$, curve degree, genus) to which our results apply.
