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math.AG2026
Border rank=rank for Kruskal tensors and a Kruskal's theorem for skew decompositions
Alexander Taveira Blomenhofer, Benjamin Lovitz
We show that border rank is equal to rank for Kruskal tensors. We also give an analogous Kruskal condition for alternating tensors, which certifies uniqueness of skew rank decompos…
math.AG2025
On defectivity of joins, reducible secants and Fröberg's conjecture
Alexander Blomenhofer, Alex Casarotti
We introduce the notion of r-defectivity for a vector bundle on a quasi-projective variety. Using this tool, we prove several previously unknown cases of Fröberg's conjecture and…