Tropical and non-Archimedean Monge-Ampère equations for a class of Calabi-Yau hypersurfaces

Hultgren, Jakob,1986-Umeå universitet,Institutionen för matematik och matematisk statistik (author)

For a class of maximally degenerate families of Calabi-Yau hypersurfaces of complex projective space, we study associated non-Archimedean and tropical Monge--Ampère equations, taking place on the associated Berkovich space, and the essential skeleton therein, respectively. For a symmetric measure on the skeleton, we prove that the tropical equation admits a unique solution, up to an additive constant. Moreover, the solution to the non-Archimedean equation can be derived from the tropical solution, and is the restriction of a continuous semipositive toric metric on projective space. Together with the work of Yang Li, this implies the weak metric SYZ conjecture on the existence of special Lagrangian fibrations in our setting.

Mattias, JonssonDepartment of Mathematics, University of Michigan, Michigan, USA (author)
McCleerey, NicholasDepartment of Mathematics, University of Michigan, Michigan, USA (author)
Mazzon, EnricaDepartment of Mathematics, University of Michigan, Michigan, USA (author)
Umeå universitetInstitutionen för matematik och matematisk statistik (creator_code:org_t)

By the author/editor: Hultgren, Jakob, ...; Mattias, Jonsson; McCleerey, Nicho ...; Mazzon, Enrica

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