Tropical compactification in log-regular varieties

Abstract

In this article we define a natural tropicalization procedure for closed subsets of log-regular varieties in the case of constant coefficients and study its basic properties. This framework allows us to generalize some of Tevelev's results on tropical compactification as well as Hacking's result on the cohomology of the link of a tropical variety to log-regular varieties.Comment: 15 pages; fixed an index mistake in Thm. 1.4 and Cor. 1.5 and improved the exposition; to appear in Math. Zeitschrif