Cao and Zheng's tropical Griffiths conjecture
Cao and Zheng's tropical Griffiths conjecture
Let , and be positive integers such that , where
Let be a tropical algebraically nondegenerate tropical holomorphic curve. Assume that tropical hypersurfaces are defined by homogeneous tropical polynomials with degrees , respectively, such that the least common multiple of is . Let
and suppose that
Cao and Zheng's tropical Griffiths conjecture. The defect sum satisfies
This is proposed as the tropical version of Griffiths' conjecture, following the tropical version of the Shiffman conjecture proposed by Cao and Zheng. The statement concerns defect relations for tropical holomorphic curves intersecting tropical hypersurfaces and is not resolved in the supplied source context.
Progress summary
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Sources & referencesView supporting material
Primary source
Juho Halonen, Risto Korhonen and Galina Filipuk, “Tropical second main theorem and the Nevanlinna inverse problem”, arXiv:2305.13939 (2023).
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