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Local and global structure of effective and cuspidal loci on Grassmannians
KTH, Superseded Departments, Mathematics.
2003 (English)In: Communications in Algebra, ISSN 0092-7872, E-ISSN 1532-4125, Vol. 31, no 8, 3993-4006 p.Article in journal (Refereed) Published
Abstract [en]

We introduce effective loci, which are central for the study of differential systems, in a very general setting. The greater generality makes them useful in a wider range of situations; and it also makes their study more straightforward, and convenient technically. Our treatment of effective loci is based on families of relative tangents. Such families give rise, in natural ways, to Semple sheaves, and hence allow us to construct the higher contact loci by straightforward iteration. Our main result is a local description of generic effective loci, on key Grassmannians for geometric applications. We show, by means of very natural frames, that these effective loci are precisely where certain generic matrices become symmetric.

Place, publisher, year, edition, pages
2003. Vol. 31, no 8, 3993-4006 p.
Keyword [en]
effective loci, Grassmannians, higher contact loci, semple sheaves, torsors
Identifiers
URN: urn:nbn:se:kth:diva-22720DOI: 10.1081/agb-120022451ISI: 000184561000019OAI: oai:DiVA.org:kth-22720DiVA: diva2:341418
Note
QC 20100525Available from: 2010-08-10 Created: 2010-08-10Bibliographically approved

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