The characteristic numbers of cuspidal plane cubics in $\mathbb P^3$
Hernández, Xavier ; Miret, Josep M.
Bull. Belg. Math. Soc. Simon Stevin, Tome 10 (2003) no. 1, p. 115-124 / Harvested from Project Euclid
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We obtain the characteristic numbers of the variety of non degenerate cuspidal plane cubics in $\mathbb P^3$, namely, the non-zero intersection numbers which arise from considering 10 (possibly repeated) conditions from among the following: $P$, that the cuspidal cubic go through a point; $\nu$, that the cuspidal cubic intersect a line; and $\rho$, that the cuspidal cubic be tangent to a plane. In order to reach this goal, we consider a suitable compactification of the variety of non degenerate cuspidal plane cubics in $\mathbb P^3$ and we calculate, using several degeneration formulae, some of its non-zero intersection numbers, including all the characteristic ones.
Publié le : 2003-01-14
Classification:  cuspidal cubics,  characteristic numbers,  14N10,  14C17 
@article{1047309418,
     author = {Hern\'andez, Xavier and Miret, Josep M.},
     title = {The characteristic numbers of cuspidal plane 
cubics in $\mathbb P^3$},
     journal = {Bull. Belg. Math. Soc. Simon Stevin},
     volume = {10},
     number = {1},
     year = {2003},
     pages = { 115-124},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1047309418}
}

Hernández, Xavier; Miret, Josep M. The characteristic numbers of cuspidal plane 
cubics in $\mathbb P^3$. Bull. Belg. Math. Soc. Simon Stevin, Tome 10 (2003) no. 1, pp.  115-124. http://gdmltest.u-ga.fr/item/1047309418/