$V_5$中扭三次体的Kontsevich紧化的去奇异化
A desingularization of Kontsevich's compactification of twisted cubics in $V_5$
摘要：
根据定义，del Pezzo $3$ -fold $V_5$是$\mathrm{Gr}(2,5)$与$\mathbb{P}^9$中三个超平面在Plücker嵌入下的交集。在Fano几何的各种内容中研究了$V_5$中的有理曲线。本文给出了$V_5$中扭三次曲线的Kontsevich紧化和Simpson紧化的一个显式双有理关系.作为直接推论，我们得到了Kontsevich紧化的一个去奇异化模型，它导出了Kontsevich空间的交上同调群。
英文摘要：
By definition, the del Pezzo $3$-fold $V_5$ is the intersection of $\mathrm{Gr}(2,5)$ with three hyperplanes in $\mathbb{P}^9$ under the Plücker embedding. Rational curves in $V_5$ have been studied in various contents of Fano geometry. In this paper, we propose an explicit birational relation of the Kontsevich and Simpson compactifications of twisted cubic curves in $V_5$. As a direct corollary, we obtain a desingularized model of Kontsevich compactification which induces the intersection cohomology group of Kontsevich's space.
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