稀疏零点定理、复数的结果和行列式

arXiv - MATH - Commutative Algebra Pub Date : 2024-07-18 DOI:arxiv-2407.13450

Carlos D'Andrea, Gabriela Jeronimo

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引用次数: 0

摘要

我们完善并扩展了图特曼的一个结果，即在与其支持相关的环状变中，由无共同零点的稀疏劳伦多项式的有限序列所满足的 B\'ezoutidentity 的支持。当这些多项式的个数比环境空间的维数多一个时，我们得到了一个计算稀疏结果的公式，作为科斯祖尔型复数的判定式。

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Sparse Nullstellensatz, resultants and determinants of complexes

We refine and extend a result by Tuitman on the supports of a B\'ezout identity satisfied by a finite sequence of sparse Laurent polynomials without common zeroes in the toric variety associated to their supports. When the number of these polynomials is one more than the dimension of the ambient space, we obtain a formula for computing the sparse resultant as the determinant of a Koszul type complex.

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arXiv - MATH - Commutative Algebra

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