Hilbert Functions of Chopped Ideals
Fuente:
arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866909414438469632 |
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| author | Gesmundo, Fulvio Kayser, Leonie Telen, Simon |
| author_facet | Gesmundo, Fulvio Kayser, Leonie Telen, Simon |
| contents | A chopped ideal is obtained from a homogeneous ideal by considering only the generators of a fixed degree. We investigate cases in which the chopped ideal defines the same finite set of points as the original one-dimensional ideal. The complexity of computing these points from the chopped ideal is governed by the Hilbert function and regularity. We conjecture values for these invariants and prove them in many cases. We show that our conjecture is of practical relevance for symmetric tensor decomposition. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_02560 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Hilbert Functions of Chopped Ideals Gesmundo, Fulvio Kayser, Leonie Telen, Simon Commutative Algebra Algebraic Geometry 13D02, 13C40, 14N07, 65Y20 A chopped ideal is obtained from a homogeneous ideal by considering only the generators of a fixed degree. We investigate cases in which the chopped ideal defines the same finite set of points as the original one-dimensional ideal. The complexity of computing these points from the chopped ideal is governed by the Hilbert function and regularity. We conjecture values for these invariants and prove them in many cases. We show that our conjecture is of practical relevance for symmetric tensor decomposition. |
| title | Hilbert Functions of Chopped Ideals |
| topic | Commutative Algebra Algebraic Geometry 13D02, 13C40, 14N07, 65Y20 |
| url | https://arxiv.org/abs/2307.02560 |