User colin ingalls - MathOverflow most recent 30 from http://mathoverflow.net 2013-06-20T02:01:11Z http://mathoverflow.net/feeds/user/30654 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/72083/minimal-resolution-of-log-del-pezzo-surfaces/118928#118928 Answer by Colin Ingalls for Minimal resolution of Log del Pezzo surfaces Colin Ingalls 2013-01-14T22:58:24Z 2013-01-14T22:58:24Z <p>I am not sure exactly what you mean when you say log del Pezzo, but if you have klt singularities then they are quotient singularities in dimension two. For a fixed index there is a finite number of possible groups that can occur and therefore a finite number of minimal resolutions. So there is a bound in terms of the index. You can look in Nikulin, "Del Pezzo surfaces with log-terminal singularies, I" and work out an bound: $$1+ \sum\left(\frac{b_i}{2}-1\right) \leq l$$ where $b_i=-E_i^2$ and $E_i$ are the curves in the minimal resolution.</p>