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Arithmetically Cohen-Macaulay Sets of Points in P^1 x P^1

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Abstract

The interpolation problem is a significant motivating problem in algebraic geometry and commutative algebra. Naively, the goal of the interpolation problem is to consider a collection of points in some ambient space, perhaps with some restrictions, and to describe all the polynomials that vanish at this collection. Introductions to this problem can be found in [7, 28, 62, 75]. The interpolation problem has applications to other areas of mathematics, including splines [30] and coding theory [40, 57].

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Notes

  1. 1.

    Note that because \(\mathbb{P}^{1} \times \mathbb{P}^{1}\) (the case investigated by Giuffrida, et al.) is isomorphic to the quadric surface \(\mathcal{Q}\) in \(\mathbb{P}^{3}\), this variation can also be viewed as studying the interpolation problem on hypersurfaces; the paper of Huizenga [66] considers similar questions

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Authors and Affiliations

  1. Dipartimento di Matematica e Informatica, University of Catania, Catania, Italy

    Elena Guardo

  2. Department of Mathematics and Statistics, McMaster University, Hamilton, ON, Canada

    Adam Van Tuyl

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  1. Elena Guardo
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  2. Adam Van Tuyl
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Guardo, E., Van Tuyl, A. (2015). Introduction. In: Arithmetically Cohen-Macaulay Sets of Points in P^1 x P^1. SpringerBriefs in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-319-24166-1_1

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