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 Plücker embedding, and rational curves in \(V_5\) have been examined in various studies on Fano geometry. In this paper, we propose an explicit birational relation for the Kontsevich and Simpson compactifications of twisted cubic curves in \(V_5\). As a direct corollary, we obtain a desingularized model of Kontsevich compactification that induces the intersection cohomology group of Kontsevich’s space.
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Notes
i.e., the dimension of the non-zero subsheaf of F is the same as that of F.
i.e., an irreducible component of C mapping to a point under f.
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Acknowledgements
The author gratefully acknowledges the many helpful suggestions of In-Kyun Kim and SangHyeon Lee during the preparation of the paper. The author would like to thank the anonymous referee for valuable comments and suggestions to improve the quality of the paper. Data sharing not applicable to this article as no datasets were generated or analysed during the current study.
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Chung, K. Desingularization of Kontsevich’s compactification of twisted cubics in \(V_5\). manuscripta math. 171, 347–367 (2023). https://doi.org/10.1007/s00229-022-01382-2
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DOI: https://doi.org/10.1007/s00229-022-01382-2