Desingularization of Kontsevich’s compactification of twisted cubics in V5

Abstract

By definition, the del Pezzo 3-fold V5 is the intersection of Gr (2 , 5) with three hyperplanes in P9 under Plücker embedding, and rational curves in V5 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 V5. As a direct corollary, we obtain a desingularized model of Kontsevich compactification that induces the intersection cohomology group of Kontsevich’s space.