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

MathSciNet review:
2957205

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Abstract | References | Similar Articles | Additional Information

Abstract: Given a subspace of a vector space , the Kalman variety consists of all matrices of that have a nonzero eigenvector in . Ottaviani and Sturmfels described minimal equations in the case that and conjectured minimal equations for . We prove their conjecture and describe the minimal free resolution in the case that , 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 .

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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

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.