An algorithm and supporting toolkit for numerical irreducible decomposition of multiprojective varieties, reducing the computation to curves in affine space and generalizing prior work from two to arbitrarily many projective factors.
Representable Chow classes of a product of projective spaces
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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.
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A numerical toolkit for multiprojective varieties
An algorithm and supporting toolkit for numerical irreducible decomposition of multiprojective varieties, reducing the computation to curves in affine space and generalizing prior work from two to arbitrarily many projective factors.