Theorem

Alexander-Hirschowitz Theorem

Algebra

The Alexander-Hirschowitz theorem describes when a collection of double points in projective space imposes independent conditions on the homogeneous polynomials defining hypersurfaces of a given dimension, generalizing classical polynomial interpolation in several variables to points with higher multiplicities. The theorem gives a complete answer along with a short, known list of exceptional cases where the expected count of independent conditions fails to hold.

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Statement

The Alexander-Hirschowitz theorem shows that a specific collection of k double points in the projective space Pr will impose independent types of conditions on homogenous polynomials and the hypersurface of dimension d with many known lists of exceptions. 1

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Algebraic Geometry

Source Alexander-Hirschowitz theorem (Wikipedia)

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1. Alexander-Hirschowitz theorem (Wikipedia)

Introduction

Quote, Introduction

The Alexander-Hirschowitz theorem shows that a specific collection of k double points in the projective space Pr will impose independent types of conditions on homogenous polynomials

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Alexander-Hirschowitz theorem (Wikipedia)

In Group: Polynomials and Elementary Algebra, Lead section
will impose independent types of conditions on homogenous polynomials and the hypersurface of dimension d with many
In Branch: Algebraic Geometry, Lead section
shows that a specific collection of k double points in the projective space Pr will impose independent types of conditions

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Alexander-Hirschowitz Theorem

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