The Alexander–Hirschowitz Theorem and Related Problems

Huy Tài Hà () and Paolo Mantero ()
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Huy Tài Hà: Department of Mathematics, Tulane University
Paolo Mantero: University of Arkansas, Department of Mathematical Sciences

A chapter in Commutative Algebra, 2021, pp 373-427 from Springer

Abstract: 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.

Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-89694-2_12

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DOI: 10.1007/978-3-030-89694-2_12

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