Multisegment duality, canonical bases and total positivity.
Semicanonical basis generators of the cluster algebra of type .
Multiplicative properties of projectively dual varieties.
Simple Vertices of Maximal Minor Polytopes
Singularities of hyperdeterminants
We study the singular locus of the variety of of an arbitrary format. Our main result is a classification of irreducible components of the singular locus. Equivalently, we classify irreducible components of the singular locus for the projectively dual variety of a product of several projective spaces taken in the Segre embedding.
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