Representable Chow classes of a product of projective spaces

2016/12/01 by Federico Castillo, Castillo, Federico, Binglin Li +3 · 2 citations
Mathematics · #Advanced Combinatorial Mathematics #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #math.AG #math.CO

paper · pdf · doi:10.48550/arxiv.1612.00154

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

openalex publication_date 2016/12/01 · arxiv created 2020/05/19 · arxiv updated 2020/05/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• When are multidegrees positive?

Cited by

• Orbits in (ℙ^r)ⁿ and equivariant quantum cohomology
• When are multidegrees positive?

Related

• Polymatroidal tilings and the Chow class of linked projective spaces
• Chow classes of matroids and standard Young tableaux
• Representation theory for polymatroids
• On a theorem of Lafforgue
• Chow polynomials of rank-uniform labeled posets