7 problems

Kim's pseudolinearity conjecture. Every minimal type is either linear, or not even $k$-linear for any $k$.

Let $V$ be a Fano orbifold, meaning a compact Kähler orbifold whose Ricci-form cohomology class is represented by a positive $(1,1)$-form. In the quasi-regular setting, $V$ is the…

Let $(X,\alpha)$ be a compact Kähler manifold, and consider the positivity conditions denoted by $(\mathrm{SW1})$ in the source, together with their generalizations. Lejmi–Székelyh…

A solvsoliton is an algebraic Ricci soliton on a simply connected solvable Lie group. The solvsoliton linear stability conjecture. Every solvsoliton is linearly stable with respect…

Let $\mathcal{E}$ denote the Coulomb energy, let $f^*$ be an optimizer, and let $\tau$ range over translations. For a function $f$, write $f\circ\tau^{-1}$ for its translate. Guo's…

Lejmi–Székelyhidi's conjecture. These inequalities should be sufficient for the Donaldson equation to have a solution. The inequalities depend only on the cohomology classes…

Let $X$ be a compact complex manifold and $L$ an ample line bundle, so that $(X,L)$ is a polarized manifold. The class $c_1(L)$ is the first Chern class of $L$, and consider the ex…