论文标题
在Fano完整交集的各种线上的猜想上
On a Conjecture on the Variety of Lines on a Fano Complete Intersection
论文作者
论文摘要
Debarre-de Jong的猜想预测，在$ \ Mathbb {p}^n $中，流畅的Fano Hypersurface上的Fano各种线始终是预期的维度。我们将此猜想推广到Fano完成交集的情况下，并证明，对于Fano完成$ X \ subset \ Mathbb {p}^n $的HyperSurfaces的$ X \ subset \ Mathbb {p}^n $，其学位总和最多为7，$ x $上的fano品种各种线的范围都有预期的尺寸。
The Debarre-de Jong conjecture predicts that the Fano variety of lines on a smooth Fano hypersurface in $\mathbb{P}^n$ is always of the expected dimension. We generalize this conjecture to the case of Fano complete intersections and prove that for a Fano complete intersection $X\subset \mathbb{P}^n$ of hypersurfaces whose degrees sum to at most 7, the Fano variety of lines on $X$ has the expected dimension.
