Skeleta of Affine Hypersurfaces
arXiv:1211.5263 · doi:10.2140/gt.2014.18.1343
Abstract
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.
41 pages, 3 figure