Higher convexity for complements of tropical varieties Academic Article

abstract

• 2015, Springer-Verlag Berlin Heidelberg. We consider Gromovs homological higher convexity for complements of tropical varieties, establishing it for complements of tropical hypersurfaces and curves, and for nonarchimedean amoebas of varieties that are complete intersections over the field of complex Puiseux series. Based on these results, we conjecture that the complement of a tropical variety has this higher convexity, and prove a weak form of this conjecture for the nonarchimedean amoeba of any variety over the complex Puiseux field. One of our main tools is Jonssons limit theorem for tropical varieties.

authors

• Sottile, Frank

published proceedings

• Mathematische Annalen

author list (cited authors)

• Nisse, M., & Sottile, F.

citation count

• 5

complete list of authors

• Nisse, Mounir||Sottile, Frank

publication date

• June 2016

publisher

• Springer Nature  Publisher

published in

• Mathematische Annalen  Journal

keywords

• 49 Mathematical Sciences
• 4904 Pure Mathematics

Digital Object Identifier (DOI)

• 10.1007/s00208-015-1256-2

start page

• 1

end page

• 12

volume

• 365

issue

• 1-2

URL

• http://dx.doi.org/10.1007/s00208-015-1256-2