Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On prehomogeneity of a rank variety


Authors: Masaya Ouchi, Michio Hamada and Tatsuo Kimura
Journal: Proc. Amer. Math. Soc. 140 (2012), 4127-4129
MSC (2010): Primary 11S90; Secondary 15A03
Published electronically: April 13, 2012
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: If a linear algebraic group $ G$ acts on $ M(m,n)$, then it also acts on a rank variety $ M^{(r)}(m,n)=\{ X\in M(m,n)\vert\ {\rm rank}\, X=r\}$. In this paper, we give the necessary and sufficient condition that this variety has a Zariski-dense $ G$-orbit. We consider everything over the complex number field $ \mathbb{C}.$


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 11S90, 15A03

Retrieve articles in all journals with MSC (2010): 11S90, 15A03


Additional Information

Masaya Ouchi
Affiliation: Institute of Mathematics, University of Tsukuba, Ibaraki, 305-8571, Japan
Email: msy2000@math.tsukuba.ac.jp

Michio Hamada
Affiliation: Institute of Mathematics, University of Tsukuba, Ibaraki, 305-8571, Japan
Email: mhamada@math.tsukuba.ac.jp

Tatsuo Kimura
Affiliation: Institute of Mathematics, University of Tsukuba, Ibaraki, 305-8571, Japan
Email: kimurata@math.tsukuba.ac.jp

DOI: http://dx.doi.org/10.1090/S0002-9939-2012-11525-4
PII: S 0002-9939(2012)11525-4
Keywords: Rank, Zariski-dense orbit, prehomogeneous vector space
Received by editor(s): May 26, 2011
Published electronically: April 13, 2012
Communicated by: Lev Borisov
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.