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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Some results on tropical compactifications


Authors: Mark Luxton and Zhenhua Qu
Journal: Trans. Amer. Math. Soc. 363 (2011), 4853-4876
MSC (2010): Primary 14E25; Secondary 14T99
Published electronically: April 8, 2011
MathSciNet review: 2806694
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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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Additional Information

Mark Luxton
Affiliation: Department of Mathematics, University of Texas at Austin, Austin, Texas 78712
Email: mluxton@math.utexas.edu

Zhenhua Qu
Affiliation: Department of Mathematics, University of Texas at Austin, Austin, Texas 78712
Address at time of publication: Department of Mathematics, East China Normal University, Shanghai 200241, People’s Republic of China
Email: zhqu@math.ecnu.edu.cn

DOI: http://dx.doi.org/10.1090/S0002-9947-2011-05254-2
PII: S 0002-9947(2011)05254-2
Keywords: Tropical compactification, Schön variety
Received by editor(s): March 22, 2009
Received by editor(s) in revised form: October 11, 2009, and November 18, 2009
Published electronically: April 8, 2011
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.