Desingularization of Kontsevich's compactification of twisted cubics in V5

초록

By definition, the del Pezzo 3-fold V-5 is the intersection of Gr(2, 5) with three hyperplanes in P-9 under Plucker 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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