an:00058253
Zbl 0815.14002
Belghiti, Mohamed
The variety of infinitely near points of order \(n\) to points of the plane
FR
C. R. Acad. Sci., Paris, S??r. I 314, No. 7, 541-545 (1992).
00159766
1992
j
14B10 14C05
infinitely near points; Hilbert scheme
For each integer \(n \geq 1\), a variety \(S_ n\) is defined, which parametrizes the infinitely near points of order \(n\), to points of the projective plane \(P\): one has \(S_ 1 = P\), \(S_{n+1} = \text{Proj}_{S_ n} E_ n\), with \(E_ n\) a locally free \({\mathcal O}_{S_ n}\)-module of rank two. A divisor \(Y_ n\) of \(S_ n\) and an embedding of \(S_ n - Y_ n\) in the Hilbert scheme \(\text{Hilb}_ nP\) are described, \(S_ 4\) is studied more closely and some results of Halphen for the number of points of a plane curve satisfying a given differential equation are interpreted.