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

{"title":"稀疏零点定理、复数的结果和行列式","authors":"Carlos D'Andrea, Gabriela Jeronimo","doi":"arxiv-2407.13450","DOIUrl":null,"url":null,"abstract":"We refine and extend a result by Tuitman on the supports of a B\\'ezout\nidentity satisfied by a finite sequence of sparse Laurent polynomials without\ncommon zeroes in the toric variety associated to their supports. When the\nnumber of these polynomials is one more than the dimension of the ambient\nspace, we obtain a formula for computing the sparse resultant as the\ndeterminant of a Koszul type complex.","PeriodicalId":501475,"journal":{"name":"arXiv - MATH - Commutative Algebra","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2024-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Sparse Nullstellensatz, resultants and determinants of complexes\",\"authors\":\"Carlos D'Andrea, Gabriela Jeronimo\",\"doi\":\"arxiv-2407.13450\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We refine and extend a result by Tuitman on the supports of a B\\\\'ezout\\nidentity satisfied by a finite sequence of sparse Laurent polynomials without\\ncommon zeroes in the toric variety associated to their supports. When the\\nnumber of these polynomials is one more than the dimension of the ambient\\nspace, we obtain a formula for computing the sparse resultant as the\\ndeterminant of a Koszul type complex.\",\"PeriodicalId\":501475,\"journal\":{\"name\":\"arXiv - MATH - Commutative Algebra\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-07-18\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - MATH - Commutative Algebra\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2407.13450\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Commutative Algebra","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2407.13450","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

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。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文

微信好友朋友圈 QQ好友复制链接

本刊更多论文

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.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

arXiv - MATH - Commutative Algebra

自引率

0.00%

发文量

期刊最新文献

Resolutions over strict complete resolutions Regularity of Koszul modules The Existence of MacWilliams-Type Identities for the Lee, Homogeneous and Subfield Metric The complete integral closure of a Prüfer domain is a topological property Ideals, representations and a symmetrised Bernoulli triangle