# Equations and syzygies of some Kalman varieties

```@article{Sam2012EquationsAS,
title={Equations and syzygies of some Kalman varieties},
author={Steven V. Sam},
journal={arXiv: Commutative Algebra},
year={2012},
volume={140},
pages={4153-4166}
}```
• Steven V. Sam
• Published 29 May 2011
• Mathematics
• arXiv: Commutative Algebra
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…
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