Abstract
We survey old and new approaches to the study of symbolic powers of ideals. Our focus is on the symbolic Rees algebra of an ideal, viewed both as a tool to investigate its symbolic powers and as a source of challenging problems in its own right. We provide an invitation to this area of investigation by stating several open questions.
Dedicated to David Eisenbud on the occasion of his 75th birthday.
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Acknowledgements
The first author is supported by NSF grant DMS-2001445, now DMS-2140355. The second author is supported by NSF grant DMS-2101225. We thank Craig Huneke for help with tracking down the history of the terminology “symbolic Rees algebra”, and José Gonzalez for discussions regarding Mori dream spaces. We also thank Thomas Polstra for pointing us to [66], Elena Guardo for finding a typo in a previous version of the paper, and Kazuhiko Kurano for his comments on a previous version and for pointing us to [109]. Finally, we thank Anurag Singh for very detailed comments on an earlier version of the survey.
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Grifo, E., Seceleanu, A. (2021). Symbolic Rees Algebras. In: Peeva, I. (eds) Commutative Algebra. Springer, Cham. https://doi.org/10.1007/978-3-030-89694-2_11
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