3 problems

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Non-existence conjecture for ovoids in finite classical dual polar spaces
Ovoid non-existence conjecture. No ovoid exists in any finite classical dual polar space of rank at least three.
Conjectureopendual-polar-spaces finite-geometry ovoidsarXiv posted 2 days ago
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Existence conjecture for hemisystems of $\mathsf{DQ}(6,q)$
Let $q$ be an odd prime power, and let a hemisystem of the dual polar space $\mathsf{DQ}(6,q)$ mean the object discussed in the paper. Existence conjecture. For each odd prime powe…
Conjectureopendual-polar-spaces finite-geometry hemisystemsarXiv posted 2 days ago
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Nonexistence conjecture for hemisystems of dual polar spaces $\mathsf{DW}(5,q)$
Let $q$ be a prime power, and let a hemisystem of the dual polar space $\mathsf{DW}(5,q)$ mean the object discussed in the paper. Nonexistence conjecture. There are no hemisystems…
Conjectureopendual-polar-spaces finite-geometry hemisystemsarXiv posted 2 days ago

Non-existence conjecture for ovoids in finite classical dual polar spaces