5 problems

Symplecticity conjecture. For sufficiently large $k$, the transverse hyperplane sections of $F_k$ are symplectic submanifolds of $X$.

Let $X$ be a complex projective manifold of dimension $n>0$, let $j:X\hookrightarrow P=\mathbb{P}^{N}(\mathbb{C})$ be an arithmetically normal embedding, and let $\{W_p\}_{p=0}^n$…

Embedding conjecture. Every regular polar space admits a tight embedding.

Let $\mathbb{F}$ be a field, let $A_{n,\{1,n\}}(\mathbb{F})$ be the Lie incidence geometry, and let $\varepsilon_{\mathrm{nat}}$ denote its natural embedding. An embedding is absol…

The Weyl embedding conjecture. The Weyl embedding $\widehat{e}^W_n$ of $\widehat{\mathcal{Q}}_n$ induces on $\widetilde{\mathcal{Q}}_n$ its veronesean embedding $\widetilde{e}^W_n$…