Classification of log del Pezzo surfaces of index $\le 2$

Details Classification of log del Pezzo surfaces of index $\le 2$ Classification of log del Pezzo surfaces of index $\le 2$

2004-06-25

arxiv.org/abs/math/0406536v6

Mathematics

Algebraic Geometry

142 pages, many figures. An expanded and improved version of this manuscript was published in Memoirs of the Mathematical Soci

Scientific paper

This is an expanded version of our work [AN88], 1988, in Russian. We classify del Pezzo surfaces over C with log terminal singularities of index \le 2. By classification, we understand a description of the intersection graph of all exceptional curves on an appropriate (somewhat stronger than minimal) resolution of singularities together with the subgraph of the curves which are contracted to singular points. The final results are similar to classical results about classification of non-singular del Pezzo surfaces and use the usual finite root systems. However, the intermediate considerations use the theory of K3 surfaces (especially of K3 surfaces with non-symplectic involutions) and the theory of reflection groups in hyperbolic spaces (especially or reflection groups of hyperbolic lattices). As an ``elementary'' application, our results permit one to classify sextics in P^2 with simple singularities and a component of geometric genus \ge 2.

Affiliated with

Also associated with

No associations

Rating

Classification of log del Pezzo surfaces of index $\le 2$ does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Classification of log del Pezzo surfaces of index $\le 2$, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Classification of log del Pezzo surfaces of index $\le 2$ will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-206525