Tropical geometry for Nagata's conjecture and Legendrian curves

Kalinin, Nikita

doi:10.13097/archive-ouverte/unige:80308

2015

DOI: 10.13097/archive-ouverte/unige:80308

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Tropical geometry for Nagata's conjecture and Legendrian curves

Nikita Kalinin¹

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2021

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Scattering Diagrams from Holomorphic Discs in Log Calabi-Yau Surfaces

Bardwell-Evans¹,

Cheung²,

Hong³

et al. 2021

Preprint

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We construct special Lagrangian fibrations for log Calabi-Yau surfaces, and scattering diagrams from Lagrangian Floer theory of the fibres. Then we prove that the scattering diagrams recover the scattering diagrams of Gross-Pandharipande-Siebert [28] and the canonical scattering diagrams of Gross-Hacking-Keel [24]. With an additional assumption on the non-negativity of boundary divisors, we compute the disc potentials of the Lagrangian torus fibres via a holomorphic/tropical correspondence. As an application, we provide a version of mirror symmetry for rank two cluster varieties.

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Scattering Diagrams from Holomorphic Discs in Log Calabi-Yau Surfaces

Bardwell-Evans¹,

Cheung²,

Hong³

et al. 2021

Preprint

View full text Add to dashboard Cite

show abstract

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Tropical geometry for Nagata's conjecture and Legendrian curves

Cited by 1 publication

References 90 publications

Scattering Diagrams from Holomorphic Discs in Log Calabi-Yau Surfaces

Scattering Diagrams from Holomorphic Discs in Log Calabi-Yau Surfaces

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