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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Equations and syzygies of some Kalman varieties


Author: Steven V Sam
Journal: Proc. Amer. Math. Soc. 140 (2012), 4153-4166
MSC (2010): Primary 14M12, 15A18; Secondary 13P25, 13D02
Published electronically: April 26, 2012
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Abstract: Given a subspace $ L$ of a vector space $ V$, the Kalman variety consists of all matrices of $ V$ that have a nonzero eigenvector in $ L$. Ottaviani and Sturmfels described minimal equations in the case that $ \dim L = 2$ and conjectured minimal equations for $ \dim L = 3$. We prove their conjecture and describe the minimal free resolution in the case that $ \dim L = 2$, as well as some related results. The main tool is an exact sequence which involves the coordinate rings of these Kalman varieties and the normalizations of some related varieties. We conjecture that this exact sequence exists for all values of $ \dim L$.


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Additional Information

Steven V Sam
Affiliation: Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
Email: ssam@math.mit.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-2012-11593-X
PII: S 0002-9939(2012)11593-X
Received by editor(s): June 3, 2011
Published electronically: April 26, 2012
Communicated by: Harm Derksen
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.