Two Twodimensional Terminations
Abstract
Varieties with log terminal and log canonical singularities are considered in the Minimal Model Program, see \cite{...} for introduction. In \cite{shokurov:hyp} it was conjectured that many of the interesting sets, associated with these varieties have something in common: they satisfy the ascending chain condition, which means that every increasing chain of elements terminates. Philosophically, this is the reason why two main hypotheses in the Minimal Model Program: existence and termination of flips should be true and are possible to prove. In this paper we prove that the following two sets satisfy the ascending chain condition: 1. The set of minimal log discrepancies for $K_X+B$ where $X$ is a surface with log canonical singularities. 2. The set of groups $(b_1,...b_s)$ such that there is a surface $X$ with log canonical and numerically trivial $K_X+\sum b_jB_j$. The order on such groups is defined in a natural way.
 Publication:

arXiv eprints
 Pub Date:
 June 1992
 arXiv:
 arXiv:alggeom/9206005
 Bibcode:
 1992alg.geom..6005A
 Keywords:

 Mathematics  Algebraic Geometry
 EPrint:
 25 pages, 4 figures, LaTeX 2.09