Doubly-Exponential Growth of the Number of Vectors of Multipilicities for Solutions of Systems of Polynomial期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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Doubly-Exponential Growth of the Number of Vectors of Multipilicities for Solutions of Systems of Polynomial

Authors:	D Yu Grigoriev

Institution:	(1) IMR, Université de Rennes, Beaulien, 35042 Rennes, France;(2) St.Petersburg Department of the, Steklov Mathematical Institute, Russia

Abstract:	Earlier, D. Yu. Grigoriev and N. N. Vorob'yov obtained an upper bound $d^{O(\left( {_n^{n + d} } \right))}$ for the number of vectors of multiplicities for solutions of systems of the form $g1 = \cdots = gn = 0$ (assuming that the system has a finite number of solutions). In the system above, $g1, \ldots ,gn \in FX1, \ldots ,Xn]$ are polynomials of degrees $\deg (gi) \leqslant d$ . In the present paper, we show that the order of growth of this bound is close to the exact one. In particular, in the case d=n, the construction provides a doubly-exponential (in n) number of vectors of multiplicities. Bibliography: 4 titles.

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