3 problems

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Classification conjecture for maximal affine spaces of alternating matrices
Let $r=2s$ , let $\bbF$ be the underlying field, and let $\mathcal{V}$ be a trivial-spectrum linear subspace of $\operatorname{M}_s(\bbF)$ with dimension $\frac{s(s-1)}{2}$ . Conside…
Conjecturerefutedalternating-matrices constant-rank-matrices matrix-spacesarXiv posted 2 days ago
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The conjecture for the maximal dimension of constant-rank matrix spaces
Constant-rank matrix dimension conjecture. Then
Conjectureopenconstant-rank-matrices linear-algebraic-geometry vector-bundlesarXiv posted 2 days ago
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The conjecture that skew-symmetric matrix spaces of co-rank two have dimension at most four
Let $V$ be a vector space of dimension $2c+2$ , and let $A\subseteq \wedge^2 V$ be a linear space of skew-symmetric matrices of constant rank $2c$ , equivalently of co-rank $2$ . In t…
Conjectureopenconstant-rank-matrices skew-symmetric-matrices vector-bundlesarXiv posted 2 days ago

Classification conjecture for maximal affine spaces of alternating matrices