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- W2617225902 abstract "In this paper, we shall study finite generation of symbolic Rees rings of the defining ideal ${frak p}$ of the space monomial curve $(t^a, t^b, t^c)$ for pairwise coprime integers $a$, $b$, $c$. Suppose that the base field is of characteristic $0$ and the above ideal ${frak p}$ is minimally generated by three polynomials. Under the assumption that the homogeneous element $xi$ of the minimal degree in ${frak p}$ is the negative curve, we determine the minimal degree of an element $eta$ such that the pair ${ xi, eta }$ satisfies Huneke's criterion in the case where the symbolic Rees ring is Noetherian. By this result, we can decide whether the symbolic Rees ring ${cal R}_s({frak p})$ is Notherian using computers. We give a necessary and sufficient conditions for finite generation of the symbolic Rees ring of ${frak p}$ under some assumptions. We give an example of an infinitely generated symbolic Rees ring of ${frak p}$ in which the homogeneous element of the minimal degree in ${frak p}^{(2)}$ is the negative curve. We give a simple proof to (generalized) Huneke's criterion." @default.
- W2617225902 created "2017-06-05" @default.
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- W2617225902 date "2017-05-27" @default.
- W2617225902 modified "2023-09-23" @default.
- W2617225902 title "Infinitely generated symbolic Rees rings of space monomial curves having negative curves" @default.
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- W2617225902 doi "https://doi.org/10.48550/arxiv.1705.09865" @default.
- W2617225902 hasPublicationYear "2017" @default.
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