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Approximate Commutative Algebra pp 163–192Cite as

Ideal Interpolation: Translations to and from Algebraic Geometry

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Abstract

In this survey I will discuss four themes that surfaced in multivariate interpolation and seem to have analogues in algebraic geometry. The hope is that mixing these two areas together will benefit both.

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Acknowledgment

When you don’t know where you’re going, every road will take you there.

(Common sense)

First and foremost, I want to thank Carl de Boor who introduced me to the subject; patiently and tirelessly coached me in the way of thinking, talking and writing about ideal projectors and provided much needed encouragement in the last four years. I also want to thank a number of algebraic geometers who served as anonymous referees for my papers. Their friendly advice and criticisms added a lot to my understanding of the relationship between AG and AT. If this paper does not reflect this understanding, the fault is not theirs but entirely my own. I am grateful to Gregory McColm and Tom McKinley for reading the manuscript and correcting my English. Finally, I want to thank John Abbott, Anna Bigatti, Martin Kreuser and Lorenzo Robbiano who took a chance at allowing me to tango with the audience at this ApCoA conference.

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Authors and Affiliations

  1. Department of Mathematics & Statistics, University of South Florida, 33620, Tampa, FL, USA

    Boris Shekhtman

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  1. Boris Shekhtman
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Correspondence to Boris Shekhtman .

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Editors and Affiliations

  1. Dipto. Matematica, Università Genova, Via Dodecaneso 35, Genova, 16146, Italy

    Lorenzo Robbiano

  2. Dipto. Matematica, Università Genova, Via Dodecaneso 35, Genova, 16146, Italy

    John Abbott

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Shekhtman, B. (2009). Ideal Interpolation: Translations to and from Algebraic Geometry. In: Robbiano, L., Abbott, J. (eds) Approximate Commutative Algebra. Texts and Monographs in Symbolic Computation. Springer, Vienna. https://doi.org/10.1007/978-3-211-99314-9_6

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