# Fano schemes for generic sums of products of linear forms

@article{Ilten2016FanoSF,
title={Fano schemes for generic sums of products of linear forms},
author={Nathan Owen Ilten and Hendrik Suss},
journal={Journal of Algebra and Its Applications},
year={2016}
}
• Published 21 October 2016
• Mathematics
• Journal of Algebra and Its Applications
We study the Fano scheme of [Formula: see text]-planes contained in the hypersurface cut out by a generic sum of products of linear forms. In particular, we show that under certain hypotheses, linear subspaces of sufficiently high dimension must be contained in a coordinate hyperplane. We use our results on these Fano schemes to obtain a lower bound for the product rank of a linear form. This provides a new lower bound for the product ranks of the [Formula: see text] Pfaffian and [Formula: see…

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