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On a sharp bound for the regularity index of any set of fat points

✍ Scribed by Giuliana Fatabbi; Anna Lorenzini

Publisher: Elsevier Science
Year: 2001
Tongue: English
Weight: 178 KB
Volume: 161
Category: Article
ISSN: 0022-4049
DOI: 10.1016/s0022-4049(00)00083-9

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✦ Synopsis

We propose an upper bound for the regularity index of fat points of P n with no geometric conditions on the points. Whenever the conjecture is true, the bound is sharp. It is, in fact, reached when there are points with high multiplicities either on a line or on some rational curve. Besides giving an easy proof of the conjecture in P 2 , we prove it in P 3 , by using some preliminary results which hold, more generally, in P n .

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