A note on the topology of Minkowski sums and complete intersections

We discuss mixed faces of Minkowski sums of polytopes, and show that any stable complete intersection of pointed hypersurfaces is homotopy Cohen–Macaulay, generalizing a result of Hacking, and answering the topological (or weak) version of a question of Markwig and Yu. In particular, the complete intersection has the homotopy type of a wedge of spheres of the same dimension.

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K.A. has received funding from the European Research Council under the European Union’s Seventh Framework Programme ERC Grant agreement Horizon Europe ERC Grant number: 101045750 / Project acronym: Hodge-GeoComb.

Received 2 July 2022

Accepted 2 February 2023

Published 26 March 2024