A Remark on Classical Pluecker's formulae

Abstract

For any reduced curve $C\subset {\mathbb{P}}^2$, we define the notions of the number of its virtual cusps $c_v$ and the number of its virtual nodes $n_v$ which are non-negative, coincide respectively with the numbers of ordinary cusps and nodes in the case of cuspidal curves, and if $\hat{C}$ is the dual curve of an irreducible curve $C$ and ${\hat{n}}_v$ and ${\hat{c}}_v$ are the numbers of its virtual nodes and virtual cusps, then the integers $c_v$, $n_v$, ${\hat{c}}_v$, ${\hat{n}}_v$ satisfy Classical Plücker's formulae.

arXiv comment8 pages