Hilbert-Kunz functions in a family: Line-\(S_4\) quartics
type: Item
instance of: scholarly article
title: Hilbert-Kunz functions in a family: Line-\(S_4\) quartics
zbMATH Open document ID: 0932.13011
published in: Journal of Algebra
publication date: 1999-02-18T00:00:00Z
review text: With the notation of the previous review (Zbl 0932.13010) let \(G\) be a line-\(S_4.\) Then it is shown that the nondegenerate \(G\)-quartics are parametrized by \(F.\) For an appropriate \(G\) each nondegenerate \(G\)-quartic is a constant multiple of \(h_a = az^4 + (x^2 + yz)(y^2 + xz)\), \(a \in F.\) For each \(a\) the author attaches an integer \(l = l(a)\) that determines completely \(e_n(h_a).\) In particular, it turns out that \(c(h_a) = 3 + 4^{-2l}.\) The surprise is the definition of \(l = l(a).\) The author constructs a \(1\)-parameter family of dynamical systems parametrized by \(F.\) Then \(l(a)\) is defined to be an `escape time' for the system corresponding to \(a.\)
reviewed by: Peter Schenzel
Mathematics Subject Classification ID: 13D40
Mathematics Subject Classification ID: 13A35
Mathematics Subject Classification ID: 14H10
Mathematics Subject Classification ID: 13F20
zbMATH DE Number: 1221667
zbMATH Keywords: Hilbert-Kunz function
zbMATH Keywords: Hilbert-Kunz multiplicity
zbMATH Keywords: plane quartic
zbMATH Keywords: dynamical systems
MaRDI profile type: Publication
full work available at URL: jabr.1998.7517
OpenAlex ID: W2593969774
cites work: Hilbert-Kunz functions in a family: Point-\(S_4\) quartics
DOI: 10.1006/JABR.1998.7517
Recommended article: Hilbert-Kunz functions in a family: Point-\(S_4\) quartics
Recommended article: On the Hilbert-Kunz function of \(z^D-p_{4}(x,y)\)
Recommended article: The Hilbert-Kunz density functions of quadric hypersurfaces
Recommended article: The Hilbert function of curves on certain smooth quartic surfaces
Recommended article: On \(K\)-derived quartics
Recommended article: Q4527734
Recommended article: On Weierstrass points of a family of quartic curves
Recommended article: On Hilbert-Kunz functions of some hypersurfaces
Recommended article: The Hilbert-Kunz function of some quadratic quotients of the Rees algebra
author: Paul Monsky
description: scientific article; zbMATH DE number 1221667