Abstract
We study the existence of Khovanskii-finite valuations for rational curves of arithmetic genus two. We provide a semiexplicit description of the locus of degree rational curves in of arithmetic genus two that admit a Khovanskii-finite valuation. Furthermore, we describe an effective method for determining if a rational curve of arithmetic genus two defined over a number field admits a Khovanskii-finite valuation. This provides a criterion for deciding if such curves admit a toric degeneration. Finally, we show that rational curves with a single unibranch singularity are always Khovanskii-finite if their arithmetic genus is sufficiently small.
Citation
Nathan Ilten. Ahmad Mokhtar. "Khovanskii-Finite Rational Curves of Arithmetic Genus 2." Michigan Math. J. 73 (5) 1059 - 1082, November 2023. https://doi.org/10.1307/mmj/20216048
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