4 papers
Computing zero-dimensional tropical varieties via projections
Paul Görlach, Yue Ren, Leon Zhang
We present an algorithm for computing zero-dimensional tropical varieties using projections. Our main tools are fast unimodular transforms of lexicographical Gröbner bases. We prov…
Detecting tropical defects of polynomial equations
Paul Görlach, Yue Ren, Jeff Sommars
We introduce the notion of tropical defects, certificates that a system of polynomial equations is not a tropical basis, and provide two algorithms for finding them in affine space…
Tritangents and Their Space Sextics
Turku Ozlum Celik, Avinash Kulkarni, Yue Ren +1
Two classical results in algebraic geometry are that the branch curve of a del Pezzo surface of degree 1 can be embedded as a space sextic curve and that every space sextic curve h…
Tropicalized quartics and canonical embeddings for tropical curves of genus 3
Marvin Anas Hahn, Hannah Markwig, Yue Ren +1
Brodsky, Joswig, Morrison and Sturmfels showed that not all abstract tropical curves of genus can be realized as a tropicalization of a quartic in the euclidean plane. In this…