Generic consistency and nondegeneracy of vertically parametrized systems
Year: 2025
Type: article
Abstract: We determine the generic consistency, dimension and nondegeneracy of the zero locus over C ⁎ , R ⁎ and R > 0 of vertically parametrized systems: parametric polynomial systems consisting of linear combinations of monomials scaled by free parameters. These systems generalize sparse systems with fixed monomial support and freely varying parametric coefficients. As our main result, we establish the equivalence among three key properties: the existence of nondegenerate zeros, the zero set having generically the expected dimension, and the system being generically consistent. Importantly, we prove that checking whether a vertically parametrized system has these properties amounts to an easily computed matrix rank condition.
Source: Journal of Algebra
Institutions: University of Copenhagen, Universidad Politécnica de Madrid
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,310
Funders: European Commission, Novo Nordisk, Ministerio de Ciencia e Innovación, Novo Nordisk Fonden, Ministerio de Asuntos Económicos y Transformación Digital, Gobierno de España, European Research Council, Horizon 2020, European Regional Development Fund, Agencia Estatal de Investigación, H2020 Marie Skłodowska-Curie Actions, HORIZON EUROPE European Research Council
Awards: G1650125035, G1700354366, The Algebraic Geometry of Chemical Reaction Networks: Structural conditions for uniquely determined Sign-sensitivities., Signs, polynomials, and reaction networks, G4235700875, G434337789, The Algebraic Geometry of Chemical Reaction Networks: Structural conditions for uniquely determined Sign-sensitivities., G490073602, G4951254936, G5999746622, G8710511776
OpenAlex ID: W4409763057