Toricity of vertically parametrized systems with applications to reaction network theory

Elisenda Feliu; Oskar Henriksson

doi:10.48550/arXiv.2411.1513

Toricity of vertically parametrized systems with applications to reaction network theory

Department of Mathematical Sciences

Research output: Working paper › Preprint

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Abstract

In this paper, we present new necessary conditions and sufficient conditions for the (positive parts of) the varieties of vertically parametrized systems to admit monomial parametrizations. The conditions are based on a combination of polyhedral geometry and previously known results about injectivity of monomial maps. The motivation arises from the study of steady state varieties of reaction networks, as toricity simplifies the determination of multistationarity substantially.

Original language	English
Publisher	arXiv preprint
Number of pages	28
DOIs	https://doi.org/10.48550/arXiv.2411.1513
Publication status	Published - 2024

Bibliographical note

28 pages, 3 figures. Improvements in the exposition. Comments welcome!

Keywords

math.AG
14M25, 14A10, 14A25, 14Q30, 14P10

Access to Document

10.48550/arXiv.2411.1513Licence: CC BY

FulltextFinal published version, 758 KBLicence: CC BY

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Cite this

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abstract = " In this paper, we present new necessary conditions and sufficient conditions for the (positive parts of) the varieties of vertically parametrized systems to admit monomial parametrizations. The conditions are based on a combination of polyhedral geometry and previously known results about injectivity of monomial maps. The motivation arises from the study of steady state varieties of reaction networks, as toricity simplifies the determination of multistationarity substantially. ",

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AB - In this paper, we present new necessary conditions and sufficient conditions for the (positive parts of) the varieties of vertically parametrized systems to admit monomial parametrizations. The conditions are based on a combination of polyhedral geometry and previously known results about injectivity of monomial maps. The motivation arises from the study of steady state varieties of reaction networks, as toricity simplifies the determination of multistationarity substantially.

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