Abstract

Let Δ_n be the discriminant of a general polynomial of degree n and \(\mathcal{N}\) be the Newton polytope of Δ_n. We give a geometric proof of the fact that the truncations of Δ_n to faces of \(\mathcal{N}\) are equal to products of discriminants of lesser n degrees. The proof is based on the blow-up property of the logarithmic Gauss map for the zero set of Δ_n.

中文翻译：

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判别式的因式分解几何

摘要

令_Δn是阶数为n的一般多项式的判别式，而\（\ mathcal {N} \）为_Δn的牛顿多项式。我们提供了一个几何证明，即_Δn到\（\ mathcal {N} \）的面的截断等于小于n度的判别式的乘积。该证明是基于对数高斯图的零爆炸_Δn集。