12 problems

Let $(X, D_\epsilon = \sum_{\alpha \in \mathcal A} \epsilon_\alpha D_\alpha)$ be a klt Fano Campana orbifold over a number field $F$, let $L$ be a big $\mathbb Q$-divisor on $X$, a…

Let $X$ be a smooth Fano variety over a number field $K$, and let … be a boundary divisor with weights $m_i\in\mathbb{N}$ and prime divisors $D_i$. Let $S$ be a finite set of place…

Let $(X,D_\epsilon)$ be the Campana orbifold, let $L$ be the underlying big divisor, and let $F$ and $S$ be as above. Let $\alpha((X,D_\epsilon),L)$, $a((X,D_\epsilon),L)$, and…

Let $X$ be a smooth projective variety over $\a9\mathbb{C}$ and let $D$ be a strict normal crossings divisor on $X$ with irreducible components $D_1,\ldots,D_q$. For each…

Let $(X,D)$ be a klt Campana orbifold over $K$ with a good integral model $(\mathcal{X},\mathcal{D})$ over $\mathcal{O}_{K,S}$. Let $H_{\mathcal{L}}$ be the height associated with…

Let $K$ be a number field, let $(X,D)$ be a klt Campana orbifold over $K$ with a good integral model $(\mathcal{X},\mathcal{D})$ over $\mathcal{O}_{K,S}$, and let…

The source discusses an orbifold of interest and its set of Campana points. A set is thin if it belongs to the class of exceptional sets in the relevant Hilbert-property framework.…

Let $K$ be a number field, let $(X,D_{\epsilon})$ be a smooth klt Fano Campana orbifold over $K$, and let $(\mathcal{X},\mathcal{D}_{\epsilon})$ be a regular $\mathcal{O}_{K,S}$-mo…

Assume that $(d4f3,\Delta)$ is the Campana orbifold defined by … and let $N_{\mathbf m,L}(B)$ count its Campana $\mathbb Z$-points of height $H_L$ at most $B$. Let $L$ be a big and…

Let $(X,D_\epsilon)$ be a Fano orbifold over a number field $F$, and let $(\mathcal X,\mathcal D_\epsilon)$ be a good integral model over $\operatorname{Spec}\mathcal O_{F,S}$, whe…

Let $(X,D_\epsilon)$ be a Campana orbifold over a number field $F$ such that $-(K_X+D_\epsilon)$ is ample, and let $(\mathcal X,\mathcal D_\epsilon)$ be a good integral model over…

Let $K$ be a number field with ring of integers $\mathcal{O}_K$, let $S$ contain the archimedean places, and let $\mathscr{X}\to\operatorname{Spec}\mathcal{O}_{K,S}$ be a smooth pr…