33 problems

Let $X$ be a complex manifold elliptically fibered with at worst $I_{1}$ fibers over a normal analytic variety $B$ such that … Let $\alpha,\beta\in\mathop{\mathcal{S}h}_{an}(X)$ be…

Let $X$ be the weighted Fano threefold hypersurface considered in the paper, with numerical parameter $N$, and let $a_{2}$ and $a_{3}$ be the weights defining the weighted projecti…

Let $X\to B$ be as in Theorem MMP, with $X$ a Calabi–Yau variety. Suppose that $B$ is birational to a Mori fiber space $B'\to U$ with fiber $F$, and let…

Let $k$ be a number field. A non-trivial isotrivial elliptic fibration is an elliptic fibration over $\mathbb{P}^1$ that is isotrivial but not trivial. Density conjecture. The $k$-…

Let $Z^{\mathrm{sym}}_{N,r}$ be the symmetric Hilbert modular surface, and consider each $(N,r)$ in parts (ii)–(iii) of the paper's classification theorem. A Jacobian elliptic fibr…

DHT conjecture. The surface $Y$ admits an elliptic fibration $\pi\colon Y\to\mathbb{P}^1$ and an allowable loop $\gamma\subset\mathbb{P}^1$ compatible with the $\check{L}$-quasi-po…

Mirror symmetry for lattice-polarised weak del Pezzo surfaces. The mirror to $(V,C)$ is given by an elliptic fibration $W\to\Delta$ with fibre $F_p$ such that $\phi$ is a quasi del…

Let $R\to\mathbb P^1$ be a general rational elliptic surface, and let sections mean section curves of this elliptic fibration. Transversality conjecture. Any two sections meet tran…

Relative holomorphic anomaly conjecture. The series lies in

Multisection-index conjecture. One has

Charged-multiplet conjecture. The charged multiplets $H_{ch}$ in the massless spectrum satisfy

Let $(A_i,B_i)$, for $i=1,\ldots,12$, be one of the twelve Type $i$ KSS pairs of smooth elliptic Calabi--Yau $3$-folds over $\mathbb{P}^2$. The pair is called nonbirational when no…

Let $J_i\to\mathbb{P}^2$ be the common relative Jacobian of the Type $i$ KSS pair. The Tate--Shafarevich group is the group of torsors of the Jacobian fibration that are locally tr…

Let $(A_i,B_i)$, for $i=1,\ldots,12$, be one of the twelve Type $i$ KSS pairs of smooth elliptic Calabi--Yau $3$-folds over $\mathbb{P}^2$, with elliptic fibrations…

Let $f\colon X\to Z$ be a klt-trivial fibration of relative dimension $k$, with $(X,B)$ a klt projective pair whose boundary $B$ has rational coefficients. Let $r$ be the positive…

Let … be the $((3;2),(0;0))$-twisted genus-$g$ quasimap series of ${\mathbb P}^2\times{\mathbb P}^1$, and let … with $X(q_1)=q_1(\partial B_1'/\partial q_1)/(1+B_1')$. Twisted elli…

Quasimap elliptic-fibration conjecture. For $\gamma\in H_2(B,\mathbb Z)$,

Oberdieck–Pixton conjecture. For $\gamma\in H_2(B,\mathbb Z)$,

Let $B$ be a smooth compact manifold, let $W$ be a Weierstrass fibration in … and let $\widetilde{W}\to W$ be a crepant resolution obtained by a sequence of blowups of $Z$ in smoot…

The modularity conjecture. The relative potential has the form

Let $X\to B$ be a relatively minimal elliptic threefold with section, and let $\Sigma$ be its stratified discriminant locus. The associated nonabelian gauge algebras and their repr…

Let $X\to B$ be an elliptic Calabi–Yau threefold with $\mathbb{Q}$-factorial terminal singularities $\{P\}$, the relative minimal model of a Weierstrass model $W\to B$. Assume that…

Let $Q$ be a singular point of the discriminant of an elliptic fibration. Method 1 and Katz–Vafa's method are two constructions of localized representations associated with $Q$. Lo…

Let $\pi:X\to B$ be an elliptic fibration, let $\mathsf{k}\in H_2(B,\mathbb{Z})$, and let ${\mathcal C}^{\pi}_{g,\mathsf{k}}(\gamma_1,\ldots,\gamma_n)$ be the associated relative G…

Let $\pi:X\to B$ be an elliptic fibration with section and integral fibers, let $D\subset X$ be a nonsingular divisor restricting to an elliptic fibration $\pi_D:D\to A$ over a non…