8 problems

Let $Y_t$ be a smooth fibre of a semistable degeneration with nodal central fibre $Y_0$, let $\beta\in H^{2,2}(Y_t,\mathbb{Q})$ be rational, and let…

Let $\pi:\mathcal{Y}\to\Delta$ be a $G$-equivariant semistable degeneration of Calabi–Yau threefolds with ordinary double points, and let $\widetilde{Y}_0$ be a $G$-equivariant cre…

Let $X$ be an abelian threefold, let $\hat X$ be its dual, and let ${{{{{{{{\mathcal G}}}}}}}}_{F_1,F_2}$ be the sheaf constructed from non-zero coherent sheaves $F_1,F_2$ whose Ch…

Kuga--Satake Hodge conjecture. The embedding $\iota_V$ is induced by a correspondence in $A^\ast(X\times KS(V)\times KS(V))$. This is a special case of the Hodge conjecture; the pa…

Let $\mathfrak X$ be a smooth projective tropical variety. For an integer $p$, consider the tropical cohomology groups … and let $N$ be the tropical monodromy operator between them…

Demailly's Hodge conjecture for strongly positive currents. The current $\mathscr{T}$ is a weak limit

Let a supermanifold be described by a matrix-factorization category, and let its Jacobian ideal be viewed inside Hochschild cohomology. A $(p,p)$ class is a Hodge-type class of bid…

Let $A$ be an abelian variety over an algebraic closure of $\mathbb{Q}$ with good reduction to an abelian variety $A_{0}$ over an algebraic closure of a finite field. A Hodge class…