论文标题
在某些calabi-yau和通用类型的完整交集上的常规曲线和刚性曲线
Regular and rigid curves on some Calabi-Yau and general-type complete intersections
论文作者
论文摘要
令$ x $为$ n+1 $ in $ \ m athbb p^n $的一般超出表面，或者是$ \ mathbb p^{n+1}的一般$（2，n）$完整的交叉点，n \ geq 4 $。我们在所有高度的$ x $上构建平衡的理性曲线。如果$ n = 3 $或$ g = 1 $，我们在所有高度的$ x $上构建了$ g $的刚性曲线。作为应用程序，我们在Calabi-yau三倍上构建了一些刚性捆绑包。此外，我们在$ n + 2 $ in $ \ mathbb p^n $的高度曲面上构建了一些低度平衡的理性曲线。
Let $X$ be either a general hypersurface of degree $n+1$ in $\mathbb P^n$ or a general $(2,n)$ complete intersection in $\mathbb P^{n+1}, n\geq 4$. We construct balanced rational curves on $X$ of all high enough degrees. If $n=3$ or $g=1$, we construct rigid curves of genus $g$ on $X$ of all high enough degrees. As an application we construct some rigid bundles on Calabi-Yau threefolds. In addition, we construct some low-degree balanced rational curves on hypersurfaces of degree $n + 2$ in $\mathbb P^n$.
