Academy of Mathematics and Systems Science, CAS Colloquia & Seminars
Speaker:
Jerome Hoffman 教授, Department of Mathematics, Louisiana State University
Inviter:
Title:
Quaternion Rational Surfaces
Time & Venue:
2018.10.18 9:30 N205
Abstract:
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 -bases of the generating rational curves, and create the generating sets for the rst and second syzygy modules in the graded minimal free resolutions. In addition, we show that the ideal generated by the rst syzygy module expressed in terms of moving planes is exactly the same as the ideal generated by the parametrization in the the ane ring.