Year: 2021
Type: preprint
Abstract: We revisit Schmidt's theorem connecting the Schmidt rank of a tensor with the codimension of a certain variety and adapt the proof to the case of arbitrary characteristic. We also find a sharper result of this kind for homogeneous polynomials of degree d (assuming that the characteristic does not divide d(d-1)). We then use this to relate the Schmidt rank of a homogeneous polynomial (resp., a collection of homogeneous polynomials of the same degree) with the codimension of the singular locus of the corresponding hypersurface (resp., intersection of hypersurfaces). This gives an effective version of Ananyan-Hochster's Theorem A from arXiv:1610.09268.
Source: arXiv (Cornell University)
Institution: Hebrew University of Jerusalem
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4287205374