6533b86efe1ef96bd12cc671
RESEARCH PRODUCT
Tailoring a pair of pants
Ilia ZharkovHelge RuddatHelge Ruddatsubject
General MathematicsImage (category theory)010102 general mathematicsTorusCodimensionMathematics::Geometric Topology01 natural sciencesCombinatoricsMathematics::Algebraic GeometryDiscriminantHyperplane0103 physical sciencesAmoeba (mathematics)Isotopy010307 mathematical physics0101 mathematicsMathematics::Symplectic GeometryPair of pantsMathematicsdescription
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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2021-04-01 | Advances in Mathematics |