an:04127410
Zbl 0688.14050
Miret, J. M.; Xamb??-Descamps, Sebastian
Geometry of complete cuspidal plane cubics
EN
Algebraic curves and projective geometry, Proc. Conf., Trento/Italy 1988, Lect. Notes Math. 1389, 195-234 (1989).
1989
a
14N10 51N15
enumerative theory of plane cuspidal cubics; fundamental numbers
[For the entire collection see Zbl 0667.00008.]
In his book ``Kalk??l der abz??hlenden Geometrie'' (1879; reprint 1979; Zbl 0417.51008), \textit{H. C. H. Schubert} discussed the enumerative theory of plane cuspidal cubics. Schubert's calculations rely on the method of degenerations, i.e. boundary components of the space of complete cuspidal plane cubics. The authors give detailed discussion of this space (for an algebraically closed underlying field of characteristic \(\neq 2, 3)\) and base upon this and other geometric results their enumerative computations. It turns out that there are 620 non-zero fundamental numbers, but only 391 of them were already given by Schubert.
[Unfortunately the reviewer has no access to a repeatedly quoted paper of the authors: ``On Schubert's degenerations of cuspidal cubics'', Preprint, Univ. Barcelona 1987.]
H.Havlicek
Zbl 0667.00008; Zbl 0417.51008