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Publication - Dr Farhad Babaee

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

    Citation

    Babaee, F & Huh, J, 2017, ‘A tropical approach to a generalized Hodge conjecture for positive currents.’. Duke Mathematical Journal, vol 166.

    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.

    Full details in the University publications repository