Adelic amoebas disjoint from open halfspaces

Details Adelic amoebas disjoint from open halfspaces Adelic amoebas disjoint from open halfspaces

2007-06-16

arxiv.org/abs/0706.2438v2

J. reine angew. Math. 625 (2008), 115--123.

Mathematics

Algebraic Geometry

8 pages. v2: minor typographic changes, updated references. To appear in Crelle's Journal

Scientific paper

We show that a conjecture of Einsiedler, Kapranov, and Lind on adelic amoebas of subvarieties of tori and their intersections with open halfspaces of complementary dimension is false for subvarieties of codimension greater than one that have degenerate projections to smaller dimensional tori. We prove a suitably modified version of the conjecture using algebraic methods, functoriality of tropicalization, and a theorem of Zhang on torsion points in subvarieties of tori.

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