6533b7defe1ef96bd127682f
RESEARCH PRODUCT
Skeleta of affine hypersurfaces
Nicolò SibillaEric ZaslowHelge RuddatDavid Treumannsubject
Pure mathematicsPolynomialMathematicsofComputing_GENERALAffinePolytopeComplex dimensionTopological spaceTriangulation14J70Mathematics - Algebraic GeometryComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATIONFOS: MathematicsHomotopy equivalenceAlgebraic Topology (math.AT)Mathematics - Algebraic TopologyKato–Nakayama spaceAlgebraic Geometry (math.AG)SkeletonMathematicsToric degenerationTriangulation (topology)HomotopyLog geometry14J70 14R99 55P10 14M25 14T05RetractionHypersurfaceHypersurfaceNewton polytopeSettore MAT/03 - GeometriaGeometry and TopologyAffine transformationKato-Nakayama space14R99description
A smooth affine hypersurface Z of complex dimension n is homotopy equivalent to an n-dimensional cell complex. Given a defining polynomial f for Z as well as a regular triangulation of its Newton polytope, we provide a purely combinatorial construction of a compact topological space S as a union of components of real dimension n, and prove that S embeds into Z as a deformation retract. In particular, Z is homotopy equivalent to S.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2014-01-01 |