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Summer 2021 Kähler Differentials for Fat Point Schemes in 1×1
Elena Guardo, Martin Kreuzer, Tran N. K. Linh, Le Ngoc Long
J. Commut. Algebra 13(2): 179-207 (Summer 2021). DOI: 10.1216/jca.2021.13.179

Abstract

Let 𝕏 be a set of K-rational points in 1×1 over a field K of characteristic zero, let 𝕐 be a fat point scheme supported at 𝕏, and let R𝕐 be the bihomogeneous coordinate ring of 𝕐. In this paper we investigate the module of Kähler differentials ΩR𝕐K1. We describe this bigraded R𝕐-module explicitly via a homogeneous short exact sequence and compute its Hilbert function in a number of special cases, in particular when the support 𝕏 is a complete intersection or an almost complete intersection in 1×1. Moreover, we introduce a Kähler different for 𝕐 and use it to characterize ACM reduced schemes in 1×1 having the Cayley–Bacharach property.

Citation

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Elena Guardo. Martin Kreuzer. Tran N. K. Linh. Le Ngoc Long. "Kähler Differentials for Fat Point Schemes in 1×1." J. Commut. Algebra 13 (2) 179 - 207, Summer 2021. https://doi.org/10.1216/jca.2021.13.179

Information

Received: 5 February 2018; Revised: 27 November 2018; Accepted: 9 December 2018; Published: Summer 2021
First available in Project Euclid: 30 June 2021

Digital Object Identifier: 10.1216/jca.2021.13.179

Subjects:
Primary: 13N05
Secondary: 13C40, 13D40, 14N05

Rights: Copyright © 2021 Rocky Mountain Mathematics Consortium

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Vol.13 • No. 2 • Summer 2021
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