I wonder if a semistalbe K3 surface over a $p$-adic field has a minimal semistable model. I guess yes but I do not find any reference. Also, if we have a semistable K3 surface wi …

I am mainly interested in varieties over an algebraic closed field $k$ (or $\mathbb{C}$). The classification of complex surface is established in the last century and known as Enri …

Being a not yet enrolled independently supervised graduate student in mathematics, with prospects of applying to American graduate schools hopefully in a 1-2 years' time, I have a …

Let $X$ be a complex compact Kähler minimal surface with zero algebraic dimension and $H^2(X,\mathcal{O}_X) \ne 0$. We know that according to Enriques–Kodaira classification, $X$ i …

Let X be an smooth projective variety defined over $\mathbb{C}$. In the context of the minimal model program it is often important to understand the geometry of the maps defined b …

In order get a minimal model for a given a variety , we can carry out a sequence of contractions in such a way that that every map contracts some curves on which the canonical div …

Let $k$ be an algebraically closed field of characteristic $p>0$. I have been trying to find out unsuccessfully if there is a mmp for algebraic surfaces over $k$. I know minimal s …

There are examples of elliptic fiber spaces over a two-dimensional base which have infinitely many relative minimal models (where two abstractly isomorphic models connected by flop …

Suppose all my varieties are complex threefolds $X\rightarrow Y$ over some smooth base curve germ $Y$. We can assume the fibres are Del Pezzo surfaces with generic smooth fibre. I …

I'm looking for references of explicit computation of the pseudoeffective cone $\overline{\text{Eff}}(X)$ of a projective variety $X$.

This is one of these questions where it's tempting to just leave it at the title, but let me try to define the objects in question. A conical symplectic resolution is a projective …

I'm starting to learn the minimal model program. It seems there are two definitions for a variety $X$ with only terminal singularities to be minimal. $K_X$ is nef. Every biratio …

I've been reading some papers of Namikawa lately, and have on several occasions come across a claim I would really like someone to expand on. On page 4 of Poisson deformations of …

In the next days I have to give a talk in which I need to explain some of the usual singularities of pairs that one meets when dealing with the minimal model program: KLT, DLT and …

I would like to know how much of the recent results on the MMP (due to Hacon, McKernan, Birkar, Cascini, Siu,...) which are usually only stated for varieties over the complex numbe …