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Curves on a double surface.

Scott Nollet, Enrico Schlesinger (2003)

Collectanea Mathematica

Let F be a smooth projective surface contained in a smooth threefold T, and let X be the scheme corresponding to the divisor 2F on T. A locally Cohen-Macaulay curve C included in X gives rise to two effective divisors on F, namely the largest divisor P contained in C intersection F and the curve R residual to C intersection F in C. We show that under suitable hypotheses a general deformation of R and P lifts to a deformation of C on X, and give applications to the study of Hilbert schemes of locally...

Cutting diagram method for systems of plane curves with base points

Marcin Dumnicki (2007)

Annales Polonici Mathematici

We develop a new method of proving non-speciality of a linear system with base fat points in general position. Using this method we show that the Hirschowitz-Harbourne conjecture holds for systems with base points of equal multiplicity bounded by 42.

Cycle exceptionnel de l’éclatement d’un idéal définissant l’origine de C n et applications

Alain Hénaut (1987)

Annales de l'institut Fourier

Soit I un idéal de C { z 1 , ... , z n } définissant l’origine de C n . On donne une méthode explicite pour déterminer, après un choix convenable des générateurs de I = ( f 1 , ... , f n + p ) , le cycle de P n + p - 1 sous-jacent à la fibre exceptionnelle de l’éclatement de C n relativement à I . On étudie également l’éclatement d’une famille équimultiple d’idéaux ponctuels paramétrée par un germe d’espace analytique complexe réduit.

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