| Authors: | Milićević, Luka | Affiliations: | Mathematics Mathematical Institute of the Serbian Academy of Sciences and Arts |
Title: | Low-codimensional Subvarieties Inside Dense Multilinear Varieties | First page: | 904 | Last page: | 909 | Related Publication(s): | Proceedings | Conference: | 13th European Conference on Combinatorics, Graph Theory and Applications EURO-COMB’25 | Issue Date: | 2025 | Rank: | M34 | URL: | https://site.pheedloop.com/event/Eurocomb25/Abstracts | Abstract: | Let G1, . . . , Gk be nite-dimensional vector spaces over a prime eld Fp. Let V be a va- riety inside G1 ×· · ·×Gk de ned by a multilinear map. We show that if |V |≥ c|G1|· · · |Gk|, then V contains a subvariety de ned by at most K(logp c−1 + 1) multilinear forms, where K depends on k only. This result is optimal up to multiplicative constant and is relevant to the partition vs. analytic rank problem in additive combinatorics |
Publisher: | HUN-REN Alfréd Rényi Insitute of Mathematics |
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