论文标题
相对的Bott-Samelson品种
Relative Bott-Samelson varieties
论文作者
论文摘要
我们证明，定义的关于多种标志的定义，两个相对的Bott-Samelson品种在标志束上的产物是相对Richardson品种的奇异性的分辨率。该结果概括了Brion将Richardson品种奇异性的分辨率分辨为相对环境。它反映了一种现象，即相对理查森品种的局部几何形状完全受Chan-Pflueger研究的相交相对舒伯特品种完全控制。对于相对司硕的理查森品种，我们还证明了类似的定理，从而为Brill-Noether品种提供了奇异性的分辨率，并在两次标记的椭圆形曲线上施加了后果。
We prove that, defined with respect to versal flags, the product of two relative Bott-Samelson varieties over the flag bundle is a resolution of singularities of a relative Richardson variety. This result generalizes Brion's resolution of singularities of Richardson varieties to the relative setting. It reflects the phenomenon that the local geometry of a relative Richardson variety is completely governed by the two intersecting relative Schubert varieties, studied by Chan-Pflueger. We also prove an analogous theorem in the case of relative Grassmannian Richardson varieties, thereby furnishing a resolution of singularities for the Brill-Noether variety with imposed ramification on twice-marked elliptic curves.
