Alexander-Hirschowitz内插定理的新证明
A new proof of the Alexander-Hirschowitz interpolation Theorem
摘要：
经典的多元多项式插值问题可以推广到具有更大重数的点的情形。到目前为止，我们所知道的基本上都集中在亚历山大-赫茨霍维茨定理中，该定理说，P^r中的二重点的一般集合给出了d次超曲面的线性系L上的独立条件，除了一个众所周知的例外。我们提出了这个定理的一个新的证明，它包括在执行退化的P^r和分析L如何退化。
英文摘要：
The classical polynomial interpolation problem in several variables can be generalized to the case of points with greater multiplicities. What is known, as yet, is essentially concentrated in the Alexander-Hirschowitz Theorem which says that a general collection of double points in P^r gives independent conditions on the linear system L of the hypersurfaces of degree d, with a well known list of exceptions. We present a new proof of this theorem which consists in performing degenerations of P^r and analyzing how L degenerates.
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