Summer 2020 Quaternion rational surfaces
Jerome William Hoffman, Xiaohong Jia, Haohao Wang
J. Commut. Algebra 12(2): 237-261 (Summer 2020). DOI: 10.1216/jca.2020.12.237


A quaternion rational surface is a rational surface generated by two rational space curves via quaternion multiplication. In general, the structure of the graded minimal free resolution of a rational surface is unknown. The goal of this paper is to construct the graded minimal free resolution of a quaternion rational surface generated by two rational space curves. We will provide the explicit formulas for the maps of these graded minimal free resolutions. The approach we take is to utilize the information of the μ -bases of the generating rational curves, and create the generating sets for the first and second syzygy modules in the graded minimal free resolutions. In addition, we show that the ideal generated by the first syzygy module expressed in terms of moving planes is exactly the same as the ideal generated by the parametrization in the affine ring.


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Jerome William Hoffman. Xiaohong Jia. Haohao Wang. "Quaternion rational surfaces." J. Commut. Algebra 12 (2) 237 - 261, Summer 2020.


Received: 9 March 2017; Revised: 20 August 2017; Accepted: 30 August 2017; Published: Summer 2020
First available in Project Euclid: 2 June 2020

zbMATH: 07211337
MathSciNet: MR4105546
Digital Object Identifier: 10.1216/jca.2020.12.237

Primary: 14Q05
Secondary: 13D02 , 14Q10

Keywords: graded minimal free resolution , implicit equations , syzygy

Rights: Copyright © 2020 Rocky Mountain Mathematics Consortium


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Vol.12 • No. 2 • Summer 2020
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