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

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 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.

Comments are welcome

References in corpus (3)

• Hilbert schemes of lines and conics and automorphism groups of Fano threefolds
• Geometric Manin's Conjecture and rational curves
• Rational curves and instantons on the Fano threefold $Y_5$