2 research outputs found
Open loci of ideals with applications to Birational maps
In this work we show that the loci of ideals in principal class, ideals of
grade at least two, and ideals of maximal analytic spread are Zariski open sets
in the parameter space. As an application, we show that the set of birational
maps of {\it clear polynomial degree} over an arbitrary projective variety
, denoted by \Bir(X)_{d}, is a constructible set. This extends a previous
result by Blanc and Furter.Comment: 19 pg
Hankel determinantal rings have rational singularities
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 modul