TL;DR
This paper introduces the concept of tropically unirational varieties, explores techniques for proving their tropical unirationality, and discusses the open question of whether all unirational varieties are tropically unirational.
Contribution
It defines tropically unirational varieties and provides methods and examples for establishing their tropical unirationality, addressing an open question in the field.
Findings
Several techniques for proving tropical unirationality.
Examples of tropically unirational varieties.
Open question on whether all unirational varieties are tropically unirational.
Abstract
We introduce tropically unirational varieties, which are subvarieties of tori that admit dominant rational maps whose tropicalisation is surjective. The central (and unresolved) question is whether all unirational varieties are tropically unirational. We present several techniques for proving tropical unirationality, along with various examples.
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