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- W2000720906 abstract "A primitive multiple curve is a Cohen–Macaulay irreducible projective curve Y that can be locally embedded in a smooth surface, and such that C = Y red is smooth. In this case, $${L=mathcal{I}_{C}/{mathcal{I}}_{C}^{2}}$$ is a line bundle on C. This paper continues the study of deformations of Y to curves with smooth irreducible components, when the number of components is maximal (it is then the multiplicity n of Y). If a primitive double curve Y can be deformed to reduced curves with smooth components intersecting transversally, then $${h^{0}(L^{-1}){neq}0}$$ . We prove that conversely, if L is the ideal sheaf of a divisor with no multiple points, then Y can be deformed to reduced curves with smooth components intersecting transversally. We give also some properties of reducible deformations in the case of multiplicity n > 2." @default.
- W2000720906 created "2016-06-24" @default.
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- W2000720906 date "2015-05-01" @default.
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- W2000720906 title "Reducible deformations and smoothing of primitive multiple curves" @default.
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- W2000720906 doi "https://doi.org/10.1007/s00229-015-0755-5" @default.
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