Skeleta of affine hypersurfaces

Helge Ruddat, Nicolò Sibilla, David Treumann, Eric Zaslow

Research output: Contribution to journalArticle

6 Citations (Scopus)

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

Fingerprint

Homotopy
Hypersurface
Cell Complex
Retract
Polytope
Topological space
Triangulation
n-dimensional
Union
Polynomial

Keywords

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

ASJC Scopus subject areas

  • Geometry and Topology

Cite this

Ruddat, Helge ; Sibilla, Nicolò ; Treumann, David ; Zaslow, Eric. / Skeleta of affine hypersurfaces. In: Geometry and Topology. 2014 ; Vol. 18, No. 3. pp. 1343-1395.
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Ruddat, H, Sibilla, N, Treumann, D & Zaslow, E 2014, 'Skeleta of affine hypersurfaces', Geometry and Topology, vol. 18, no. 3, pp. 1343-1395. https://doi.org/10.2140/gt.2014.18.1343

Skeleta of affine hypersurfaces. / Ruddat, Helge; Sibilla, Nicolò; Treumann, David; Zaslow, Eric.

In: Geometry and Topology, Vol. 18, No. 3, 07.07.2014, p. 1343-1395.

Research output: Contribution to journalArticle

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