Exact border subranks and tight bounds are determined for k-fold matrix multiplication and several other algebra structure tensors at all orders, together with a proof that degeneration propagates from higher to lower order.
Symmetric subrank and its border analogue
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
The symmetric subrank of homogeneous polynomial is the largest number of terms in a diagonal form to which it can be specialized by a (typically non-invertible) linear variable substitution. Building on earlier work by Derksen-Makam-Zuiddam and Biaggi-Chang-Draisma-Rupniewski for ordinary tensors, we determine the asymptotic behavior of symmetric subrank and symmetric border subrank of degree-d forms as the number of variables tends to infinity. Furthermore, by using results from geometric invariant theory we show that for cubic (resp. quartic) forms the symmetric subrank and symmetric border subrank coincide if the latter is at most three (resp. two).
citation-role summary
extension 1
citation-polarity summary
fields
math.AG 1years
2026 1verdicts
UNVERDICTED 1roles
extension 1polarities
extend 1representative citing papers
citing papers explorer
-
Border subrank of higher order tensors and algebras
Exact border subranks and tight bounds are determined for k-fold matrix multiplication and several other algebra structure tensors at all orders, together with a proof that degeneration propagates from higher to lower order.