A desingularization of Kontsevich's compactification of twisted cubics in $V_5$

Kiryong Chung

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arXiv · 1902.01658

A desingularization of Kontsevich's compactification of twisted cubics in $V_5$

Kiryong Chung

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Abstract

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 Pl\"ucker 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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BibTeX RIS

Kiryong Chung. 2019-02-05. A desingularization of Kontsevich's compactification of twisted cubics in $V_5$. https://arxiv.org/abs/1902.01658

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