5 papers
Polynomial Bounds on Degeneration Order from Commutativity Properties of Tensor Slices
Shree Ganesh, Pascal Koiran, Rafael Oliveira
A tensor has border rank at most if it can be written as where has rank at most for all sufficiently sm…
Tensor decomposition beyond uniqueness, with an application to the minrank problem
Pascal Koiran, Rafael Oliveira
We prove a generalization to Jennrich's uniqueness theorem for tensor decompositions in the undercomplete setting. Our uniqueness theorem is based on an alternative definition of t…
Rank Bounds and PIT for circuits via a non-linear Edelstein-Kelly theorem
Abhibhav Garg, Rafael Oliveira, Akash Kumar Sengupta
We prove a non-linear Edelstein-Kelly theorem for polynomials of constant degree, fully settling a stronger form of Conjecture 30 in Gupta (2014), and generalizing the main result…
Primes via Zeros: Interactive Proofs for Testing Primality of Natural Classes of Ideals
Abhibhav Garg, Rafael Oliveira, Nitin Saxena
A central question in mathematics and computer science is the question of determining whether a given ideal is prime, which geometrically corresponds to the zero set of , de…
Strong Algebras and Radical Sylvester-Gallai Configurations
Rafael Oliveira, Akash Kumar Sengupta
In this paper, we prove the following non-linear generalization of the classical Sylvester-Gallai theorem. Let be an algebraically closed field of characteristic ,…