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.
Skeleta of affine hypersurfaces / Ruddat, H.; Sibilla, N.; Treumann, D.; Zaslow, E.. - In: GEOMETRY & TOPOLOGY. - ISSN 1465-3060. - 18:3(2014), pp. 1343-1395. [10.2140/gt.2014.18.1343]
Skeleta of affine hypersurfaces
Sibilla N.;
2014-01-01
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.File in questo prodotto:
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