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We provide explicit faithful re-embeddings for all hyperelliptic curves of genus at most three and an algorithmic way to construct them. Both in the faithful tropicalization algorithm and the proofs of correctness, we showcase OSCAR-methods for commutative algebra, polyhedral and tropical geometry.

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Faithful Tropicalization of Hyperelliptic Curves

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  • 发表日期：

    2025年

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  • Hannah Markwig,
  • Lukas Ristau,
  • Victoria Schleis

摘要

We provide explicit faithful re-embeddings for all hyperelliptic curves of genus at most three and an algorithmic way to construct them. Both in the faithful tropicalization algorithm and the proofs of correctness, we showcase OSCAR-methods for commutative algebra, polyhedral and tropical geometry.