Corpus ID: 227736385

Polyhedral Homotopies in Cox Coordinates

@article{Duff2020PolyhedralHI,
  title={Polyhedral Homotopies in Cox Coordinates},
  author={Timothy Duff and Simon Telen and Elise Walker and Thomas Yahl},
  journal={arXiv: Algebraic Geometry},
  year={2020}
}
We introduce the Cox homotopy algorithm for solving a sparse system of polynomial equations on a compact toric variety $X_\Sigma$. The algorithm lends its name from a construction, described by Cox, of $X_\Sigma$ as a GIT quotient $X_\Sigma = (\mathbb{C}^k \setminus Z) // G$ of a quasi-affine variety by the action of a reductive group. Our algorithm tracks paths in the total coordinate space $\mathbb{C}^k$ of $X_\Sigma$ and can be seen as a homogeneous version of the standard polyhedral… Expand

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