9 problems

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…

Schur functor Chern character polynomiality conjecture. Each $G_i(E,\lambda)$ has degree $i$ both as an element of the Chow ring of $X$ and as a polynomial in $\lambda$. In particu…

Let $X$ be an algebraic variety, and let $H^{\bullet}(X, \mathcal{T}_{\mathrm{poly}})$ denote the cohomology of its sheaf of polyvector fields. The Grothendieck–Teichmüller group…

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…