10 problems

Gross–Pavanelli's mirror conjecture. The mirror of $X$ is $\check{X}$, and the mirror of $\check{X}$ is $Y$.

Numerical criterion for abelian fibrations. The Hilbert scheme $X$ admits a structure of an abelian fibration if and only if

Let $X\to\mathbb P^n$ be an abelian fibration, let $P\to\mathbb P^n$ be its relative Picard, and let $X_0$ be the relative Picard of $P$. Let…

Let $X^{2n}$ be an irreducible holomorphic symplectic manifold equipped with an abelian fibration whose fibres have polarization type $(1,\ldots,1,n+1)$. Assume the fibration admit…

Let $X^{2n}$ be an irreducible holomorphic symplectic manifold equipped with an abelian fibration whose fibres are isomorphic to Jacobians of curves. A multisection is a subvariety…

Let $X^{\prime}$ be an irreducible holomorphic symplectic manifold containing a non-trivial divisor $D^{\prime}$ with $q_X(D^{\prime})=0$. Let $X$ be a birational model correspondi…

Let $X$ be an irreducible holomorphic symplectic manifold, and let $q_X$ denote its Beauville–Bogomolov quadratic form. A divisor is nef if it has nonnegative intersection with eve…

Let $C$ be a smooth, projective curve over a field $k$, and let $p:A\to C$ be a smooth group scheme with irreducible fibers whose generic fiber $A_K$ is an Abelian variety. Let…

Let $X$ be a projective manifold such that the cotangent bundle $\Omega_X$ is pseudoeffective. Assume that $X$ admits an abelian fibration $f:X\to C$ onto a curve $C$, and let $F$…

Let $V_{8,w}^{1}$ be the Calabi–Yau threefold fibered by $(1,8)$-polarized abelian surfaces, with a free action of $\mathbb{Z}_{8}\times\mathbb{Z}_{8}$, and let…