9 problems

The maximal third Chern character conjecture. If $c=-1$ and $d=\frac12+\frac C5\ll0$, then

Positive Chern character conjecture. If ${\rm ch}_k(X)$ is positive for every $k\le n$, then

Let $X$ be an $n$-dimensional smooth $l$-Fano variety, meaning that $X$ is smooth and Fano and its Chern characters $\text{ch}_i(X)$ are positive for every…

Chern-character positivity conjecture. All signed Chern character numbers $(-1)^n\operatorname{Ch}_{2\lambda}$, where $|\lambda|=n$, of irreducible hyper-Kähler manifolds are posit…

The projective-space characterization conjecture. Then $X\cong \mathbb{P}^n$.

Let $X$ be a smooth toric Fano $d$-fold, and let $V^d$ denote the exceptional toric Fano variety used in the paper. A torus invariant subsurface is a torus-invariant surface…

Let $X$ be a smooth toric Fano $d$-fold. A smooth toric Fano variety is $\mathrm{ch}_2$-positive when its second Chern character has positive intersection with every relevant surfa…

Chern-character filtration conjecture.

The p-integrality conjecture. For every variety $X$, every positive integer $n$, and every prime number $p$, the displayed $p$-integrality assertion holds. The homological Chern ch…