Lovász–Saks–Schrijver ideals and coordinate sections of determinantal varieties

the Lovász-Saks-Schrijver ideal defining the $d$ -dimensional orthogonal representations of the graph complementary to $G$ , and
the determinantal ideal of the $(d + 1)$ -minors of a generic symmetric matrix with $0$ in positions prescribed by the graph $G$ .

In characteristic $0$ these two ideals turn out to be closely related and algebraic properties such as being radical, prime or a complete intersection transfer from the Lovász–Saks–Schrijver ideal to the determinantal ideal. For Lovász–Saks–Schrijver ideals we link these properties to combinatorial properties of $G$ and show that they always hold for $d$ large enough. For specific classes of graphs, such a forests, we can give a complete picture and classify the radical, prime and complete intersection Lovász–Saks–Schrijver ideals.

PDF Access Denied

We have not been able to recognize your IP address 3.133.144.197 as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription, or purchase of single articles.

Please contact your institution's librarian suggesting a subscription, for example by using our journal-recommendation form. Or, visit our subscription page for instructions on purchasing a subscription.

You may also contact us at contact@msp.org
or by using our contact form.

Or, you may purchase this single article for USD 40.00:

Keywords

determinantal rings, complete intersections, ideals associated to graphs, Gröbner bases.

Mathematical Subject Classification 2010

Primary: 05E40

Secondary: 05C62, 13P10

Milestones

Received: 8 February 2018

Revised: 3 November 2018

Accepted: 24 December 2018

Published: 2 March 2019

Authors

Aldo Conca
Dipartimento di Matematica Università di Genova 16146 Genova Italy

Volkmar Welker
Fachbereich Mathematik und Informatik Philipps-Universität Marburg 35032 Marburg Germany

Vol. 13, No. 2, 2019

Aldo Conca and Volkmar Welker

Abstract

PDF Access Denied

Keywords

Mathematical Subject Classification 2010

Milestones

Authors