6 problems

The LQEL classification conjecture. $X$ is obtained by taking linear sections and/or isomorphic projections of a rational homogeneous manifold in its natural minimal embedding.

Let $X=G/P$ be a rational homogeneous variety, let $W^P$ denote the relevant set of Schubert representatives, and let $n=|W^P|$, the number of Schubert varieties in $X$. A strong c…

Rational-homogeneity conjecture. The manifold $X$ should be rational-homogeneous, equivalently, there should exist an embedding

Let $l\geq 2$, let $V$ be the irreducible representation of $\mathfrak{sl}(l+1,\mathbb R)$ with highest weight $\rho=\omega_1+\omega_2+\dots+\omega_l$, and let the corresponding ra…

Width-decreasing conjecture. Let $X$ be a CP-manifold which is not a product of positive-dimensional varieties. If $\tau(X)>0$, then there exists a surjective morphism $f:X'\to X$…

The paper studies homogeneous vector bundles on rational homogeneous varieties $G/P$ of type $ADE$. For a homogeneous bundle $E$, let $\operatorname{gr}E$ be its associated graded…