7 problems

Let $X$ be a smooth projective variety, let $B^2_{\mathrm{hom}}(X)$ denote the codimension-two Griffiths group with rational coefficients modulo algebraic equivalence, and suppose…

Let $X$ be a hyper-Kähler variety. Let $B^\ast(X)$ be the ring of algebraic cycles with rational coefficients modulo algebraic equivalence, and let $c_j(T_X)$ denote the Chern clas…

Let $Z_1$ and $Z_2$ be the cycles described earlier in the source, assume that they are homologous, and suppose that they satisfy the vanishing condition denoted by equation (10sep…

Let $X$ be a hyperkähler variety. Let $B^*(X)$ be the ring of cycles with rational coefficients modulo algebraic equivalence, and let $E^*(X)\subset B^*(X)$ be the $\mathbb Q$-suba…

Let $X$ be a smooth projective variety, let $A^i(X)=CH^i(X)_{\mathbb Q}$ denote codimension-$i$ cycles modulo rational equivalence, and let $F^iA^i(X)$ be the deepest level of the…

Let $Y$ be a smooth projective variety and let $F$ be a Bloch–Beilinson filtration with rational coefficients on its Chow groups. Assume that $F$ also induces a filtration on Chow…

Let $C$ be a smooth very general curve of genus $g\geq 2k+1$, and let $JC$ be its Jacobian. Write $Z_k$ for the $k$-th Beauville component of the cycle associated with $C$ in…