Sparse Nullstellensatz, resultants and determinants of complexes
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866918042346192896 |
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| author | D'Andrea, Carlos Jeronimo, Gabriela |
| author_facet | D'Andrea, Carlos Jeronimo, Gabriela |
| contents | We refine and extend a result by Tuitman on the supports of a Bezout 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_13450 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Sparse Nullstellensatz, resultants and determinants of complexes D'Andrea, Carlos Jeronimo, Gabriela Algebraic Geometry Commutative Algebra Primary 13P15, Secondary 14M25, 68W30 We refine and extend a result by Tuitman on the supports of a Bezout 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. |
| title | Sparse Nullstellensatz, resultants and determinants of complexes |
| topic | Algebraic Geometry Commutative Algebra Primary 13P15, Secondary 14M25, 68W30 |
| url | https://arxiv.org/abs/2407.13450 |