All Questions

What are some references for a beginning graduate student in algebraic geometry to learn about the minimal model program? I'm not thinking about entering this field, but rather I just want to know ...

Let $(X,B)$ be a projective log canonical pair (here I mean $B \geq 0$). Assume that the coefficients of $B$ are rational, and that $K_X+B \equiv 0$. Is it true that $K_X + B \sim_\mathbb{Q} 0$? I ...

In many articles of the minimal model program the authors work with sub-lc pairs instead of lc-pairs. In other words, they consider non-necesarilly effective boundary divisors $B$. Is it expected (...

Let $X$ be a projective variety with only normal crossing singularity. Is there a description of the derived category or the category of perfect complexes? What about the existence of semiorthogonal ...

In the course of a proof, I need some version of Castelnuovo and Artin's contractibility criteria for a family of surfaces. Say I have a family (flat is probably needed, in order to compare ...

I'm seaching for a proof of the theorem below. Do you know any reference? Consider $f:X\rightarrow Y$ projective birational map between normal varieties and $\mathbb{R}$ cartier divisor $D$ whose ...