Skeleta of Affine Hypersurfaces
Algebraic Geometry
2014-11-11 v2 Algebraic Topology
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.
Keywords
Cite
@article{arxiv.1211.5263,
title = {Skeleta of Affine Hypersurfaces},
author = {Helge Ruddat and Nicolò Sibilla and David Treumann and Eric Zaslow},
journal= {arXiv preprint arXiv:1211.5263},
year = {2014}
}
Comments
41 pages, 3 figure