Computing the characteristic numbers of the variety of nodal plane cubics in P-3
In this note we obtain, phrased in present day geometric and computational frameworks, the characteristic numbers of the family U-nod of non-degenerate nodal plane cubics in P-3, first obtained by Schubert in his Kalkul der abzahlenden Geometrie. The main geometric contribution is a detailed study of a variety X-nod, which is a compactification of the family U-nod, including the boundary components (degenerations) and a generalization to P-3 of a formula of Zeuthen for nodal cubics in P-2. The computations have been carried out with the WIRIS boost WIT. (c) 2006 Elsevier Ltd. All rights reserved.
characteristic numbers plane nodal curves effective computational methods