Fat points schemes on a smooth quadric

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Abstract

We study zero-dimensional fat points schemes on a smooth quadric Q≅P1×P1, and we characterize those schemes which are arithmetically Cohen–Macaulay (aCM for short) as subschemes of Q giving their Hilbert matrix and bigraded Betti numbers. In particular, we can compute the Hilbert matrix and the bigraded Betti numbers for fat points schemes with homogeneous multiplicities and whose support is a complete intersection (CI for short). Moreover, we find a minimal set of generators for schemes of double points whose support is aCM.

MSC

14A15
14E15
13H10
13D02
13D40

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