Affine-compact functors
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Joseph Gubeladze
Abstract
Several well known polytopal constructions are examined from the functorial point of view. A naive analogy between the Billera–Sturmfels fiber polytope and the abelian kernel is disproved by an infinite explicit series of polytopes. A correct functorial formula is provided in terms of an affine-compact substitute of the abelian kernel. The dual cokernel object is almost always the natural affine projection. The Mond–Smith–van Straten space of sandwiched simplices, useful in stochastic factorizations, leads to a different kind of affine-compact functors and new challenges in polytope theory.
Communicated by: M. Joswig
Funding: Supported by U.S. NSF grant DMS 1301487 and Georgian NSF grant DI/16/5-103/12.
Acknowledgements
I thank (i) the referee for many constructive suggestions, which greatly improved the exposition, and for spotting a number of inaccuracies, (ii) Tristram Bogart, from whom I learned about the question, attributed to someone else, whether Σ Hom(R, f) ≅ Hom(R, Σf), and (iii) Timmy Chan for Figure 1.
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Articles in the same Issue
- Frontmatter
- A Batyrev type classification of ℚ-factorial projective toric varieties
- Blocking sets of certain line sets related to a hyperbolic quadric in PG(3, q)
- Affine-compact functors
- Limit points of the branch locus of 𝓜g
- Criteria for strict monotonicity of the mixed volume of convex polytopes
- Principal curvatures and parallel surfaces of wave fronts
- Nodal curves with a contact-conic and Zariski pairs
- Corrigendum to the paper “On surfaces with two apparent double points”
Articles in the same Issue
- Frontmatter
- A Batyrev type classification of ℚ-factorial projective toric varieties
- Blocking sets of certain line sets related to a hyperbolic quadric in PG(3, q)
- Affine-compact functors
- Limit points of the branch locus of 𝓜g
- Criteria for strict monotonicity of the mixed volume of convex polytopes
- Principal curvatures and parallel surfaces of wave fronts
- Nodal curves with a contact-conic and Zariski pairs
- Corrigendum to the paper “On surfaces with two apparent double points”
