Zariski
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Related Articles from SNS
A Kronecker algorithm for locally closed sets over a perfect field
arXiv:2512.14888v2 Announce Type: replace-cross Abstract: We develop a probabilistic algorithm of Kronecker type for computing a Kronecker representation of a zero-dimensional linear section of an algebraic variety $V$ defined over a perfect field $k$. The variety $V$ is the Zariski closure of the set of common zeros $\{F_1=0,\ldots,F_r=0,G\not=0\}$ of multivariate polynomials $F_1,\ldots,F_r\in k[X_1,\ldots,X_n]$ outside a prescribed hypersurface $\{G=0\}$. We assume that $F_1,\ldots,F_r$...
Asymptotic tensor rank is characterized by polynomials
arXiv:2411.15789v2 Announce Type: replace Abstract: Asymptotic tensor rank is notoriously difficult to determine. Indeed, determining its value for the $2\times 2$ matrix multiplication tensor would determine the matrix multiplication exponent, a long-standing open problem. On the other hand, Strassen's asymptotic rank conjecture makes the bold claim that asymptotic tensor rank equals the largest dimension of the tensor and is thus as easy to compute as matrix rank.