Representable Chow classes of a product of projective spaces

Abstract

Inside a product of projective spaces, we try to understand which Chow classes come from irreducible subvarieties. The answer is closely related to the theory of integer polymatroids. The support of a representable class can be (partially) characterized as some integer point inside a particular polymatroid. If the class is multiplicity-free, we obtain a complete characterization in terms of representable polymatroids. We also generalize some of the results to the case of products of Grassmannians.

This has been generalized and expanded in another paper that also includes additional coauthors, available at arXiv:2005.07808

Cited by in corpus (2)

• Mustafin varieties, moduli spaces and tropical geometry
• Orbits in $({\mathbb{P}}^r{)}^n$ and equivariant quantum cohomology