DC Field | Value | Language |
dc.contributor.author | Bruns, Winfried | |
dc.contributor.author | Conca, Aldo | |
dc.date.accessioned | 2021-12-23T16:08:29Z | - |
dc.date.available | 2021-12-23T16:08:29Z | - |
dc.date.issued | 2009 | |
dc.identifier.issn | 00218693 | |
dc.identifier.uri | https://osnascholar.ub.uni-osnabrueck.de/handle/unios/8317 | - |
dc.description.abstract | Let V and W be vector spaces of dimension m and n respectively. We investigate the Zariski closure X(t) of the image Y(t) of the map Hom(K) (V, W) -> Hom(K) (boolean AND(t) V, boolean AND(t) W), phi -> boolean AND(t) phi. In the case t = min(m, n), Y(t) = X(t) is the cone over a Grassmannian, but for 1 < t < min(m, n) one has X(t) not equal Y(t). We analyze the G = GL(V) x GL(W)-orbits in X(t) via the G-stable prime ideals in O(X(t)). It turns out that they are classified by two numerical invariants, one of which is the rank and the other a related invariant that we call small rank. Surprisingly, the orbits in X(t)Y(t) arise from the images Y(u) for u < t and simple algebraic operations. In the last section we determine the singular locus of X(t). Apart from well-understood exceptional cases, it is formed by the elements of rank <= 1 in Y(t). (C) 2008 Elsevier Inc. All rights reserved. | |
dc.language.iso | en | |
dc.publisher | ACADEMIC PRESS INC ELSEVIER SCIENCE | |
dc.relation.ispartof | JOURNAL OF ALGEBRA | |
dc.subject | Algebra of minors | |
dc.subject | ALGEBRAS | |
dc.subject | Exterior power | |
dc.subject | General linear group | |
dc.subject | Mathematics | |
dc.subject | Orbit structure | |
dc.subject | Singular locus | |
dc.title | The variety of exterior powers of linear maps | |
dc.type | journal article | |
dc.identifier.doi | 10.1016/j.jalgebra.2008.03.024 | |
dc.identifier.isi | ISI:000271350300003 | |
dc.description.volume | 322 | |
dc.description.issue | 9 | |
dc.description.startpage | 2927 | |
dc.description.endpage | 2949 | |
dc.contributor.orcid | 0000-0001-5897-9985 | |
dc.publisher.place | 525 B ST, STE 1900, SAN DIEGO, CA 92101-4495 USA | |
dcterms.isPartOf.abbreviation | J. Algebra | |
dcterms.oaStatus | Bronze, Green Submitted, Green Published | |
crisitem.author.dept | FB 06 - Mathematik/Informatik | - |
crisitem.author.deptid | fb06 | - |
crisitem.author.parentorg | Universität Osnabrück | - |
crisitem.author.netid | BrWi827 | - |