Abstract
In this paper we deal with singularities of the linear systems of plane curves passing through S, where S is a zerodimensional closed subscheme of degree n of P 2=P 2 k ,k an algebraically closed field of any characteristic. We determine the least degree of a nonsingular curve passing through S, when S is in uniform position.
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References
M.G. CINQUEGRANI,Nonsingular curves passing through a zerodimensional subscheme of P 2, Comm. in Algebra (to appear)
J.P. JONANOLOU,Theorems de Bertini et applications, Birchaüser, n. 42 (1983)
R. MAGGIONI and A. RAGUSA,Nonsingular curves passing through points of P 2 in generic position, Journal of Algebra, vol. 92, n. 1 (1985)
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This paper was written while the author was member of C.N.R., Sez. 3 of G.N.S.A.G.A. and was supported by M.P.I. funds
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Cinquegrani, M.G. On singularities of the curves belonging to some linear system inP 2 . Manuscripta Math 61, 131–144 (1988). https://doi.org/10.1007/BF01259324
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DOI: https://doi.org/10.1007/BF01259324