Connectivity of tropicalizations
Dustin Cartwright, Sam Payne
TL;DR
This paper proves that the tropicalization of an irreducible variety over a complete or algebraically closed valued field is connected through codimension 1, confirming a longstanding question in algebraic geometry.
Contribution
It establishes the connectivity of tropicalizations of irreducible varieties over various fields, answering a question posed in 2003.
Findings
Tropicalizations are connected through codimension 1.
The result holds over all characteristics.
Provides a positive answer to a 2003 open problem.
Abstract
We show that the tropicalization of an irreducible variety over a complete or algebraically closed valued field is connected through codimension 1, giving an affirmative answer in all characteristics to a question posed by Einsiedler, Lind, and Thomas in 2003.
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