Geometry & Topology

Skeleta of affine hypersurfaces

Helge Ruddat, Nicolò Sibilla, David Treumann, and Eric Zaslow

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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 T 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.

Article information

Geom. Topol., Volume 18, Number 3 (2014), 1343-1395.

Received: 11 July 2013
Revised: 19 December 2013
Accepted: 17 January 2014
First available in Project Euclid: 20 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 14J70: Hypersurfaces
Secondary: 14R99: None of the above, but in this section

skeleton retraction hypersurface homotopy equivalence affine toric degeneration Kato–Nakayama space log geometry Newton polytope triangulation


Ruddat, Helge; Sibilla, Nicolò; Treumann, David; Zaslow, Eric. Skeleta of affine hypersurfaces. Geom. Topol. 18 (2014), no. 3, 1343--1395. doi:10.2140/gt.2014.18.1343.

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