Compactifications of conic spaces in del Pezzo 3-fold

摘要

Let V-5 be the del Pezzo 3-fold defined by the 6-dimensional linear section of the Grassmannian variety Gr(2, 5) under the Plucker embedding. In this paper, we present an explicit birational relation of compactifications of degree-two rational curves (i.e. conics) in V-5. By a product, we obtain the virtual Poincare polynomial of compactified moduli spaces. (C) 2019 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.