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Symmetric powers: structure, smoothability, and applications (2408.02754v1)
Published 5 Aug 2024 in math.AG, cs.CC, and math.AC
Abstract: We investigate border ranks of twisted powers of polynomials and smoothability of symmetric powers of algebras. We prove that the latter are smoothable. For the former, we obtain upper bounds for the border rank in general and prove that they are optimal under mild conditions. We give applications to complexity theory.
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