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- W4300670525 abstract "Let $I_X$ be the saturated homogeneous ideal defining a codimension two arithmetically Cohen-Macaulay scheme $X subseteq mathbb{P}^n$, and let $I_X^{(m)}$ denote its $m$-th symbolic power. We are interested in when $I_X^{(m)} = I_X^m$. We survey what is known about this problem when $X$ is locally a complete intersection, and in particular, we review the classification of when $I_X^{(m)} = I_X^m$ for all $m geq 1$. We then discuss how one might weaken these hypotheses, but still obtain equality between the symbolic and ordinary powers. Finally, we show that this classification allows one to: (1) simplify known results about symbolic powers of ideals of points in $mathbb{P}^1 times mathbb{P}^1$; (2) verify a conjecture of Guardo, Harbourne, and Van Tuyl, and (3) provide additional evidence to a conjecture of Romer." @default.
- W4300670525 created "2022-10-04" @default.
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- W4300670525 date "2016-06-02" @default.
- W4300670525 modified "2023-09-30" @default.
- W4300670525 title "Symbolic powers of codimension two Cohen-Macaulay ideals" @default.
- W4300670525 doi "https://doi.org/10.48550/arxiv.1606.00935" @default.
- W4300670525 hasPublicationYear "2016" @default.
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