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Systèmes linéaires de courbes planes à singularités ordinaires imposées

✍ Scribed by Thierry Mignon

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
315 KB
Volume
327
Category
Article
ISSN
0764-4442

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✦ Synopsis

Nous kudions I'irr~ductibilitC et la lissitk de la courbe plane gknkrique de degrd d passant par T points gCnCriques du plan avec des multiplicitts ml, . . ? m, fixCes par avance. Nous prksentons un thCori?me montrant que, si les multiplicitks sont < 3 et le degrk assez grand, ces courbes sont irkductibles et lisses en dehors des T singularit& impo&es. 0 Acadkmie des SciencesElsevier, Paris Linear system of plane curves with ordinary prescribed singularities

We study the irreducibility and the smoothness of the generic plane curve of degree d passing through r generic points with prescribed multiplicities mi. We prove that, under the assumptions that the multiplicities are at most 3 and the degree is high enough, these curves are irreducible and smooth away from the prescribed singularities. 0 AcadCmie des Sciences/Elsevier, Paris

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