Skeleta of affine hypersurfaces

Helge Ruddat, Nicolò Sibilla, David Treumann, Eric Zaslow

Research output: Contribution to journalArticlepeer-review

10 Scopus citations

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 TΔ of its Newton polytope Δ, 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.

Original languageEnglish (US)
Pages (from-to)1343-1395
Number of pages53
JournalGeometry and Topology
Volume18
Issue number3
DOIs
StatePublished - Jul 7 2014

Keywords

  • Affine
  • Homotopy equivalence
  • Hypersurface
  • Kato-Nakayama space
  • Log geometry
  • Newton polytope
  • Retraction
  • Skeleton
  • Toric degeneration
  • Triangulation

ASJC Scopus subject areas

  • Geometry and Topology

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