0000000000377145

AUTHOR

Ilia Zharkov

showing 2 related works from this author

Compactifying Torus Fibrations Over Integral Affine Manifolds with Singularities

2021

This is an announcement of the following construction: given an integral affine manifold B with singularities, we build a topological space X which is a torus fibration over B. The main new feature of the fibration X → B is that it has the discriminant in codimension 2.

Pure mathematicsMathematics::Algebraic GeometryDiscriminantFeature (computer vision)FibrationTorusAffine transformationCodimensionTopological spaceAffine manifoldMathematics::Symplectic GeometryMathematics
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Tailoring a pair of pants

2021

Abstract We show how to deform the map Log : ( C ⁎ ) n → R n such that the image of the complex pair of pants P ∘ ⊂ ( C ⁎ ) n is the tropical hyperplane by showing an (ambient) isotopy between P ∘ ⊂ ( C ⁎ ) n and a natural polyhedral subcomplex of the product of the two skeleta S × Σ ⊂ A × C of the amoeba A and the coamoeba C of P ∘ . This lays the groundwork for having the discriminant to be of codimension 2 in topological Strominger-Yau-Zaslow torus fibrations.

General MathematicsImage (category theory)010102 general mathematicsTorusCodimensionMathematics::Geometric Topology01 natural sciencesCombinatoricsMathematics::Algebraic GeometryDiscriminantHyperplane0103 physical sciencesAmoeba (mathematics)Isotopy010307 mathematical physics0101 mathematicsMathematics::Symplectic GeometryPair of pantsMathematicsAdvances in Mathematics
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