Uniform bounds on projective dimension and Castelnuovo-Mumford regularity
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866914561871839232 |
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| author | Caviglia, Giulio De Stefani, Alessandro |
| author_facet | Caviglia, Giulio De Stefani, Alessandro |
| contents | In this article we obtain uniform effective upper bounds for the projective dimension and the Castelnuovo-Mumford regularity of homogeneous ideals inside a standard graded polynomial ring $S$ over a field. Such bounds are independent of the number of variables of $S$, in the spirit of Stillman's conjecture and of the Ananyan-Hochster's theorem, and depend on partial data extracted from the beginning or the end of the resolution. In this direction, we extend a result of McCullough from 2012 regarding a bound on regularity in terms of half the syzygies to a bound on the projective dimension and the regularity of an ideal in terms of a fraction of the syzygies. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_12787 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Uniform bounds on projective dimension and Castelnuovo-Mumford regularity Caviglia, Giulio De Stefani, Alessandro Commutative Algebra In this article we obtain uniform effective upper bounds for the projective dimension and the Castelnuovo-Mumford regularity of homogeneous ideals inside a standard graded polynomial ring $S$ over a field. Such bounds are independent of the number of variables of $S$, in the spirit of Stillman's conjecture and of the Ananyan-Hochster's theorem, and depend on partial data extracted from the beginning or the end of the resolution. In this direction, we extend a result of McCullough from 2012 regarding a bound on regularity in terms of half the syzygies to a bound on the projective dimension and the regularity of an ideal in terms of a fraction of the syzygies. |
| title | Uniform bounds on projective dimension and Castelnuovo-Mumford regularity |
| topic | Commutative Algebra |
| url | https://arxiv.org/abs/2409.12787 |