8 problems

Let $M\subset\mathbb{P}^{n-1}(\mathbb{Q})$ be a thin set of type II, and let $N_{\mathbb{P}^{n-1}}(M,B)$ denote the number of points of $M$ of height at most $B$. Projective type I…

Let $\pi:\mathcal X\to B$ be a good Fano fibration and let $\mathsf Z\subset\mathcal X_{\eta}(K(B))$ be the exceptional set. A properly constructible thin set is a finite union of…

Let $\pi:\mathcal{X}\to B$ be a good Fano fibration, let $\mathcal{X}_{\eta}$ be its generic fiber, and let $\mathsf Z$ be the union of the images of all breaking thin maps into…

Let $X$ be a geometrically uniruled, geometrically integral, smooth projective variety over a number field $F$, and let $L$ be a big and nef $\mathbb Q$-divisor on $X$. Assume that…

Lehmann–Tanimoto's conjecture. Considering all such morphisms $f$ for which $f^*L$ is not big or

Let $X$ be a smooth uniruled variety over a number field $F$ and let $L$ be a big and nef $\mathbb Q$-divisor on $X$. For every $F$-morphism $f:Y\to X$ from a smooth projective var…

Let $X$ be a smooth projective variety over a number field $F$ with ample anticanonical class $-K_X$. Let $\mathcal{L}=(L,\|\cdot\|)$ be a big and nef adelically metrized line bund…

Let $G\subset S_n$ be a transitive subgroup, let $X=(\mathbb{P}^m)^n/G$, and assume $m\cdot\operatorname{ind}(G)\ge 2$. Let $X(K)^{\operatorname{prim}}$ denote the primitive $K$-po…