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The Alexander–Hirschowitz Theorem and Related Problems

In: Commutative Algebra

Author

Listed:
  • Huy Tài Hà

    (Department of Mathematics, Tulane University)

  • Paolo Mantero

    (University of Arkansas, Department of Mathematical Sciences)

Abstract

We present a proof of a celebrated theorem of Alexander and Hirschowitz determining when a general set of double points in ℙ n $$\mathbb {P}^n$$ has the expected Hilbert function. Our intended audience are Commutative Algebraists who may be new to interpolation problems. In particular, the main aim of our presentation is to provide a self-contained proof containing all details (including some we could not find in the literature). Also, considering our intended audience, we have added (a) short appendices to make this survey more accessible and (b) a few open problems related to the Alexander–Hirschowitz theorem and the interpolation problems.

Suggested Citation

  • Huy Tài Hà & Paolo Mantero, 2021. "The Alexander–Hirschowitz Theorem and Related Problems," Springer Books, in: Irena Peeva (ed.), Commutative Algebra, pages 373-427, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-89694-2_12
    DOI: 10.1007/978-3-030-89694-2_12
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