A tropical approach to a generalized Hodge conjecture for positive currents.

Farhad Babaee, June Huh

Research output: Contribution to journalArticle (Academic Journal)peer-review

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Abstract

Demailly showed that the Hodge conjecture is equivalent to the statement that any (p,p)-dimensional closed current with rational cohomology class can be approximated by linear combinations of integration currents associated to subvarieties, and asked whether any strongly positive (p,p)-dimensional closed current with rational cohomology class can be approximated by positive linear combinations of integration currents associated to subvarieties. Using tropical geometry, we construct a (p,p)-dimensional current on a smooth projective variety that does not satisfy the latter statement.
Original languageEnglish
Article number14
Pages (from-to)2749-2813
Number of pages64
JournalDuke Mathematical Journal
Volume166
Issue number14
Early online date6 Sep 2017
DOIs
Publication statusPublished - 1 Oct 2017

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