Equations and syzygies of some Kalman varieties

Sam, Steven

doi:10.1090/S0002-9939-2012-11593-X

Equations and syzygies of some Kalman varieties
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by Steven V Sam PDF

Proc. Amer. Math. Soc. 140 (2012), 4153-4166 Request permission

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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