# 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} }

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…

## 5 Citations

Equations of Kalman varieties

- Mathematics
- 2017

The Kalman variety of a linear subspace is a vector space consisting of all endomorphisms that have an eigenvector in that subspace. We resolve a conjecture of Ottaviani and Sturmfels and give the…

Matrices with eigenvectors in a given subspace

- Mathematics
- 2010

The Kalman variety of a linear subspace in a vector space consists of all endomorphism that possess an eigenvector in that subspace. We study the defining polynomials and basic geometric invariants…

USING REPRESENTATION THEORY TO CALCULATE SYZYGIES

- Mathematics
- 2015

These are lecture notes for the workshop “Syzygies of algebraic varieties” that took place November 20–22, 2015 at University of Illinois, Chicago. The goal of these lectures is to explain the method…

Tensors with eigenvectors in a given subspace

- Mathematics, Computer ScienceRendiconti del Circolo Matematico di Palermo Series 2
- 2020

This work considers the Kalman variety of tensors having singular t -tuples with the first component in a given linear subspace and proves analogous results, which are new even in the case of matrices, using Chern classes for enumerative computations.

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