7 problems

Let $k$ be the degree of a multisection in a genus-one-fibered Calabi–Yau threefold. Toric hypersurfaces realize $k=2,3$, complete intersections realize a $4$-section, and more sop…

Let $k$ be the degree of a multisection in a genus-one-fibered Calabi–Yau threefold. Toric hypersurface constructions realize only $k=2,3$, complete intersections realize a $4$-sec…

Let $B$ be a generalized del Pezzo surface with $b_2(X)=b_2(B)+1$, and let … be a smooth genus-one fibered Calabi–Yau threefold with a 5-section. Assume that $X$ is the degeneracy…

Let $B$ be the base of a genus-one fibration, let $N$ be the degree of its multisection, and let $N_k$, for $k=1,\ldots,N-1$, denote the numbers of fibral curves intersecting the…

Let the dual geometries be the genus one fibered Calabi-Yau threefolds arising as dual pairs in the constructions described above. The Tate–Shafarevich group is the group classifyi…

Genus-one fibration Jacobi-form conjecture. The quantity $Q^\beta Z_\beta$ transforms under $\Gamma_1(N)$ as a weak Jacobi form of weight zero and index

Let a Calabi–Yau variety admit a relatively minimal genus-one fibration with multiple fibers, and let a multiple fiber have multiplicity $m$. Discrete-torsion conjecture. The multi…