All Questions

My question is motivated by ideas around the moduli b-divisor of an lc-trivial fibration (see for instance the following paper by Ambro https://arxiv.org/pdf/math/0308143.pdf). In such a setup, one ...

Given a morphism between normal varieties $f: X \to Y$, we can push forward a Cartier divisor $D$ to get a cycle $f_* D$. On the other hand, we can form the line bundle $\mathscr{L}(D)$ and push that ...

Let $X$ be an irreducible $n$-dimensional projective variety, and $$Y_n\subset Y_{n-1}\subset\dots\subset Y_1\subset X$$ a flag of irreducible subvarieties such that $Y_i$ has codimension $i$ in $X$ ...

Let $X$ be a smooth projective variety, and $D\subset X$ a smooth nef and big divisor. Assume that the restriction map $Pic(X)\rightarrow Pic(D)$ is an isomorphism over $\mathbb{Q}$. Under which ...

Let $f:X\dashrightarrow Y$ be an isomorphism in codimension one between smooth projective varieties. Let $C\subset X$ a curve generating an extremal ray of the cone of moving curves $Mov_1(X)$, and ...

Let $X$ be a projective variety and $C\subset X$ be a moving curve, that is the curves numerically equivalent to $C$ cover a dense open subset of $X$. How can we detect when $C$ is an extremal ray ...