On lower bounds for the F-pure threshold of equigenerated ideals
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866911587188604928 |
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| author | Baily, Benjamin |
| author_facet | Baily, Benjamin |
| contents | Let $k$ be a field of positive characteristic and $R = k[x_0,\dots, x_n]$. We consider ideals $I\subseteq R$ generated by homogeneous polynomials of degree $d$. Takagi and Watanabe proved that $\mathrm{fpt}(I)\geq \mathrm{height}(I)/d$; we classify ideals $I$ for which equality is attained. Inspired by a result of de Fernex, Ein, and Mustaţă, we give a lower bound on $\mathrm{fpt}(I)$ in terms of the height of $τ(I^{\mathrm{fpt}(I)})$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_18891 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On lower bounds for the F-pure threshold of equigenerated ideals Baily, Benjamin Commutative Algebra 13A35 (Primary) 14B05, 52B20 (Secondary) Let $k$ be a field of positive characteristic and $R = k[x_0,\dots, x_n]$. We consider ideals $I\subseteq R$ generated by homogeneous polynomials of degree $d$. Takagi and Watanabe proved that $\mathrm{fpt}(I)\geq \mathrm{height}(I)/d$; we classify ideals $I$ for which equality is attained. Inspired by a result of de Fernex, Ein, and Mustaţă, we give a lower bound on $\mathrm{fpt}(I)$ in terms of the height of $τ(I^{\mathrm{fpt}(I)})$. |
| title | On lower bounds for the F-pure threshold of equigenerated ideals |
| topic | Commutative Algebra 13A35 (Primary) 14B05, 52B20 (Secondary) |
| url | https://arxiv.org/abs/2506.18891 |