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Skeleta of affine
hypersurfaces
Helge Ruddat, Nicolò Sibilla, David Treumann and Eric Zaslow |
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Geometry & Topology 18 (2014) 1343–1395
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Abstract |
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A smooth affine hypersurface of complex dimension is homotopy equivalent to an –dimensional cell complex. Given a defining polynomial for as well as a regular triangulation of its Newton polytope , we provide a purely combinatorial construction of a compact topological space as a union of components of real dimension , and prove that embeds into as a deformation retract. In particular, is homotopy equivalent to . |
Keywords
skeleton, retraction, hypersurface, homotopy equivalence,
affine, toric degeneration, Kato–Nakayama space, log
geometry, Newton polytope, triangulation
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Mathematical Subject Classification 2010
Primary: 14J70
Secondary: 14R99
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References |
Publication
Received: 11 July 2013
Revised: 19 December 2013
Accepted: 17 January 2014
Published: 7 July 2014
Proposed: Richard Thomas
Seconded: Benson Farb, Danny Calegari
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Authors |
| Helge Ruddat | |
| Mathematisches Institut Johannes Gutenberg-Universität Mainz Staudingerweg 9 D-55099 Mainz Germany |
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| Nicolò Sibilla | |
| Max Planck Institute for
Mathematics Vivatsgasse 7 D-53111 Bonn Germany |
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| David Treumann | |
| Department of Mathematics Boston College Carney Hall, Room 301 Chestnut Hill Boston, MA 02467-3806 USA |
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| Eric Zaslow | |
| Department of Mathematics Northwestern University 2033 Sheridan Road Evanston, IL 60208-2730 USA |
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