Fiber cones of rational normal scrolls are Cohen-Macaulay
Commutative Algebra
2021-07-13 v2 Algebraic Geometry
Abstract
In this short paper, we show that the fiber cones of rational normal scrolls are Cohen-Macaulay. As an application, we compute their Castelnuovo-Mumford regularities and -invariants, as well as the reduction number of the defining ideals of the rational normal scrolls. We also characterize the Gorensteinness of the fiber cone.
Keywords
Cite
@article{arxiv.2009.03484,
title = {Fiber cones of rational normal scrolls are Cohen-Macaulay},
author = {Kuei-Nuan Lin and Yi-Huang Shen},
journal= {arXiv preprint arXiv:2009.03484},
year = {2021}
}
Comments
Following the suggestion of experts, we split the original paper in arXiv:2009.03484v1 into two parts. And this is the first part, showing up as arXiv:2009.03484v2, with title changed. The second part regarding the regularity of the secant variety appears as arXiv:2107.04168. A result regarding Gorensteinness is new. Comments are welcome!