# The generic geometry of steady state varieties

Source: [The generic geometry of steady state varieties](<https://www.sota2.com/research/paper/68fa5cf01e209131ce9d5a5f>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2026-05-16T05:00:12.406Z

Authors: Elisenda Feliu, Oskar Henriksson, Beatriz Pascual-Escudero

Published: 2024-12-23T18:55:42.000Z

## Abstract

We answer several fundamental geometric questions about reaction networks with power-law kinetics, on topics such as generic finiteness of the number of steady states, robustness, and nondegenerate multistationarity. In particular, we give an ideal-theoretic characterization of generic absolute concentration robustness, as well as conditions under which a network that admits multiple steady states also has the capacity for nondegenerate multistationarity. The key tools underlying our results come from the theory of vertically parametrized systems, and include a linear algebra condition that characterizes when the steady state system has positive nondegenerate zeros.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2412.17798>)

[PDF](<https://arxiv.org/pdf/2412.17798.pdf>)