Some results on tropical compactifications

Luxton, Mark; Qu, Zhenhua

doi:10.1090/S0002-9947-2011-05254-2

Some results on tropical compactifications
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by Mark Luxton and Zhenhua Qu PDF

Trans. Amer. Math. Soc. 363 (2011), 4853-4876 Request permission

Abstract:

In this paper, we establish some further results on tropical compactifications. We give an affirmative answer to a conjecture of Tevelev in characteristic 0: any variety contains a Schön very affine open subvariety. Also we show that any fan supported on the tropicalization of a Schön very affine variety produces a Schön compactification. As an application, we show that the moduli space of six points of $\mathbb {P}^2$ in linear general position is Hübsch. Using toric schemes over a discrete valuation ring, we extend tropical compactifications to the nonconstant coefficient case.

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