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On the postulation of lines and a fat line

Thomas Bauer 1 Sandra Di Rocco 2 David Schmitz 3 Tomasz Szemberg 4 Justyna Szpond 4 
1 Fachbereich Mathematik und Informatik [Marburg] [Dept. of Math and Computer Science]
2 KTH - Department of Mathematics [Sweden]
3 Mathematisches Institut [Bayreuth]
4 Department of Mathematics
Abstract : In the present note we show that the union of r general lines and one fat line in P 3 imposes independent conditions on forms of sufficiently high degree d, where the bound is independent of the number of lines. This extends former results of Hartshorne and Hirschowitz on unions of general lines, and of Alad-poosh on unions of general lines and one double line.
Keywords : postulation problems fat flats Hilbert functions Serre vanishing 14F17 13D40 14N05 14C20
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Thomas Bauer, Sandra Di Rocco, David Schmitz, Tomasz Szemberg, Justyna Szpond. On the postulation of lines and a fat line. MEGA 2017 - International Conference on Effective Methods in Algebraic Geometry, Jun 2017, Nice, France. ⟨hal-01829351⟩

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