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Note on a paper of P. Philippon. (English) Zbl 0634.14002
In proposition 3.3 of his paper in Bull. Soc. Math. Fr. 114, 355-383 (1986; Zbl 0617.14001; see also the preceding review), P. Philippon has sharpened previous results of Masser and Wüstholz on the degrees of the isolated components of ideals generated by polynomials of known degree over a field of characteristic 0. Here we propose to shorten and, we hope, render the scheme of that proof more transparent by \((a)\quad returning\) to the systematic use of localization and \((b)\quad by\) defining a convolution to state the multihomogeneous Bezout theorem and to evaluate the highest homogeneous term of the Hilbert polynomial.

14A05 Relevant commutative algebra
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