Equations and syzygies of some Kalman varieties
Commutative Algebra
2012-09-04 v2 Algebraic Geometry
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.
Keywords
Cite
@article{arxiv.1105.5756,
title = {Equations and syzygies of some Kalman varieties},
author = {Steven V Sam},
journal= {arXiv preprint arXiv:1105.5756},
year = {2012}
}
Comments
13 pages, no figures; v2: Removed Remark 1.6 and corrected Corollary 2.4 and proof of Proposition 2.5. Some other minor updates