4 problems

Let $X$ be a smooth complex projective variety. Define the coniveau filtration by … where $Z\subset X$ ranges over subvarieties, and let $H^{m,i}_{\operatorname{Hdg}}(X)$ be the la…

Let $X$ be a smooth projective variety of dimension $n$, and let $L$ be an ample line bundle. Let $N^1H^i(X,\mathbb{Q})$ denote the first coniveau piece of cohomology. Hard Lefsche…

Let $X\subset\mathbb{P}^n$ be a smooth complete intersection of $r$ hypersurfaces of degrees $d_1\leq\cdots\leq d_r$, and let $H^{n-r}(X,\mathbb{Q})_{\mathrm{prim}}$ denote its pri…

Let $X$ be a smooth complex projective variety, and let $L\subset H^k(X,\mathbb{Q})$ be a sub-Hodge structure of coniveau $c$. The coniveau of a rational Hodge structure of weight…