Hankel determinantal rings have rational singularities
Commutative Algebra
2018-07-17 v3 Algebraic Geometry
Abstract
Hankel determinantal rings, i.e., determinantal rings defined by minors of Hankel matrices of indeterminates, arise as homogeneous coordinate rings of higher order secant varieties of rational normal curves; they may also be viewed as linear specializations of generic determinantal rings. We prove that, over fields of characteristic zero, Hankel determinantal rings have rational singularities; in the case of positive prime characteristic, we prove that they are F-pure. Independent of the characteristic, we give a complete description of the divisor class groups of these rings, and show that each divisor class group element is the class of a maximal Cohen-Macaulay module.
Cite
@article{arxiv.1709.05685,
title = {Hankel determinantal rings have rational singularities},
author = {Aldo Conca and Maral Mostafazadehfard and Anurag K. Singh and Matteo Varbaro},
journal= {arXiv preprint arXiv:1709.05685},
year = {2018}
}