4 problems

Let $X\subset\mathbb P^n$ be a very general complete intersection of type $(d_1,\dots,d_c)$ with $2n-c-d\geq0$, and fix a point of $X$. Chen–Lewis–Sheng's conjecture. The locus of…

Let $X\subset \mathbb P^n$ be a hypersurface of degree greater than $2n-3$. Consider the group of algebraically trivial cycles of the codimension specified in the conjecture, modul…

Lewis–Sheng dimension conjecture. The locus of points Γ-equivalent to $p$ satisfies

Let $X$ be a projective irreducible holomorphic symplectic manifold of dimension $2k$. For an integer $r$, let $\mathbb{S}_r(X)$ be the set of points in $X$ whose orbit under ratio…