Tailoring a pair of pants

Ruddat, Helge; Zharkov, Ilia

doi:10.1016/j.aim.2021.107622

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Calculating the Skeleton1

Minimal Models X Ijkl1

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2021

2024

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Cited by 8 publications

(2 citation statements)

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“…From the perspective of tropical geometry, it would be desirable to have a more elaborate modification of the SYZ fibration which makes the discriminant locus agree precisely with Π. Such a modification appears difficult, but some progress can be found in [28].…”

Section: Calculating the Skeletonmentioning

confidence: 99%

Local mirror symmetry via SYZ

Gammage

2021

Preprint

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Section: Calculating the Skeletonmentioning

confidence: 99%

Local mirror symmetry via SYZ

Gammage

2021

Preprint

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“…Indeed, given such a manifold B, Ruddat and Zharkov construct a topological space Y and torus fibration Y → B with discriminant of codimension 2 in B, inducing the given affine structure. In [RZ21a] the authors describe the strategy in the 3-dimensional case; the general results will appear in [RZ], building on the local constructions of [RZ21b].…”

Section: Minimal Models X Ijklmentioning

confidence: 99%

Toric geometry and integral affine structures in non-archimedean mirror symmetry

Mazzon¹,

Pille-Schneider²

2021

Preprint

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We study integral dlt models of a proper C((t))-variety X along a toric stratum of the special fiber. We prove that the associated Berkovich retraction -from the non-archimedean analytification of X onto the dual complex of the model -is an affinoid torus fibration around the simplex corresponding to the toric stratum, which extends results in [NXY19]. This allows us to construct new types of non-archimedean retractions for maximally degenerate families of quartic K3 surfaces and quintic 3-folds, by gluing several non-archimedean SYZ fibrations, each one toric along a codimension one stratum. We then show that the new retractions induce the same singular integral affine structures that arise on the dual complex of toric degenerations in the Gross-Siebert program, as well as on the Gromov-Hausdorff limit of the family.

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