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Paper detail

Geometric vs Algebraic Nullity for Hyperpaths

We consider the question of how the eigenvarieties of a hypergraph relate to the algebraic multiplicities of their corresponding eigenvalues. Specifically, we (1) fully describe the irreducible components of the zero-eigenvariety of a loose $3$-hyperpath (its "nullvariety"), (2) use recent results of Bao-Fan-Wang-Zhu to compute the corresponding algebraic multiplicity of zero (its "nullity"), and then (3) for this special class of hypergraphs, verify a conjecture of Hu-Ye about the relationship between the geometric (multi-)dimension of the nullvariety and the nullity.

preprint2022arXivOpen access
Joshua CooperGrant Fickes
math.CODiscrete Mathematics
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Joshua CooperGrant Fickes

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