低维判别基因座和涡卷
Low dimensional discriminant loci and scrolls
摘要：
在假定$|V|$的奇异元的轨迹${\Cal D}(X,V)$具有等于$\dim(X)-i$的余维数的条件下，对具有向量子空间$V \subseteq H^0(X,L)$跨越$L$的光滑复极化簇$(X,L)$进行了分类，其中$i=3,4,5$是最后一种情况，并且还假定$X$具有Picard数1.事实上，它被证明，这个余维不能是$\dim(X)-4$，而它是$\dim(X)-3$当且仅当$(X,L)$是一个光滑曲线上的滚动。当余维数为$\dim(X)-5$且Picard数为1时，仅出现线的格拉斯曼运动在$\Bbb P^4$或其超平面截面中的Plücker嵌入。其中一个主要的成分是计算的第一喷束涡卷和超二次纤维化的顶级陈类。还提供了这些计算的进一步结果。
英文摘要：
Smooth complex polarized varieties $(X,L)$ with a vector subspace $V \subseteq H^0(X,L)$ spanning $L$ are classified under the assumption that the locus ${\Cal D}(X,V)$ of singular elements of $|V|$ has codimension equal to $\dim(X)-i$, $i=3,4,5$, the last case under the additional assumption that $X$ has Picard number one. In fact it is proven that this codimension cannot be $\dim(X)-4$ while it is $\dim(X)-3$ if and only if $(X,L)$ is a scroll over a smooth curve. When the codimension is $\dim(X)-5$ and the Picard number is one only the Plücker embedding of the Grassmannian of lines in $\Bbb P^4$ or one of its hyperplane sections appear. One of the main ingredients is the computation of the top Chern class of the first jet bundle of scrolls and hyperquadric fibrations. Further consequences of these computations are also provided.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
