A well-known theorem by Hartshorne and Hirschowitz states that a generic configuration of lines has good postulation. So what about non-reduced configurations? Can adding a multiple line to the configuration still preserve it’s good postulation? This is the question we mainly deal with in this talk. In the first part of the talk we introduce the postulation problem for projective schemes, then we discuss the problem for the family of schemes supported on generic linear configurations, which are the ones of particular interest. In the second part of the talk we focus on the postulation of generic lines and one multiple line in projective space. We give our main theorem providing a complete description to the case of lines and a double line, then we propose a conjecture to the general case, finally we discuss what is known about the conjecture and more recent results on it.

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Meeting ID: 9086116889
Passcode: 362880