3
votes
0answers
109 views

Singularities arising from the Minimal Model Program (an algebraic point of view)

I will start the story by the end: Is there some caracterization of (some of) the singularities arasing from the Minimal Model Program (canonical, terminal, log-...) in terms of commutative algebra ? ...
1
vote
1answer
134 views

On Non F-pure ideal and Sharp F-Purity for a pair $(X, \Delta)$ where $K_X+\Delta$ is NOT $\mathbb{Q}$-Cartier

Suppose $(X,\Delta\ge 0)$ is a pair such that $(p^g-1)(K_X+\Delta)$ is an Integral Weil Divisor for some $g>0$ and $X$ is a normal variety. Define $\mathcal{L}_{e,\Delta} = \mathcal{O}_X( ...
5
votes
3answers
562 views

Basepoints in the Canonical System of Algebraic Surfaces

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 by the complete ...