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- W4287025927 abstract "Let $S$ be a polynomial ring over any field $Bbbk$, and let $P subseteq S$ be a non-degenerate homogeneous prime ideal of height $h$. When $Bbbk$ is algebraically closed, a classical result attributed to Castelnuovo establishes an upper bound on the number of linearly independent quadrics contained in $P$ which only depends on $h$. We significantly extend this result by proving that the number of minimal generators of $P$ in any degree $j$ can be bounded above by an explicit function that only depends on $j$ and $h$. In addition to providing a bound for generators in any degree $j$, not just for quadrics, our techniques allow us to drop the assumption that $Bbbk$ is algebraically closed. By means of standard techniques, we also obtain analogous upper bounds on higher graded Betti numbers of any radical ideal." @default.
- W4287025927 created "2022-07-25" @default.
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- W4287025927 date "2021-08-12" @default.
- W4287025927 modified "2023-10-18" @default.
- W4287025927 title "Bounds on the number of generators of prime ideals" @default.
- W4287025927 doi "https://doi.org/10.48550/arxiv.2108.05683" @default.
- W4287025927 hasPublicationYear "2021" @default.
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