8 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 $\{W_p\}_{p=0}^n$…

Conjecture B. Then $(M,g)$ is biholomorphically isometric to a flag manifold $(F,g_F)$.

Characteristic-free three-generators conjecture. The pair $\{M_1,M_2\}$ satisfies the three-generators property if and only if ${\cal S}$ admits a necessarily tight embedding

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 $\widetilde{e}^W_n$…

Let $m\geq 0$, let $g_m$ be the LeBrun metric on $\mathbb{C}^2$, and let $\alpha$ be a positive real number. A metric is projectively induced if it admits a Kähler immersion into s…