Mori Dream Spaces extremal contractions of K3 surfaces
Abstract
We will give a criterion to assure that an extremal contraction of a K3 surface which is not a Mori Dream Space produces a singular surface which is a Mori Dream Spaces. We list the possible N\'eron--Severi groups of K3 surfaces with this property and an extra geometric condition such that the Picard number is greater then or equal to 10. We give a detailed description of two geometric examples for which the Picard number of the K3 surface is 3, i.e. the minimal possible in order to have the required property. Moreover we observe that there are infinitely many examples of K3 surfaces with the required property and Picard number equal to 3.
Keywords
Cite
@article{arxiv.1503.01378,
title = {Mori Dream Spaces extremal contractions of K3 surfaces},
author = {Alice Garbagnati},
journal= {arXiv preprint arXiv:1503.01378},
year = {2016}
}
Comments
V2: 25 pages. Lemma 2.6 of the old version contains a mistake pointed out by an anonimous referee. It is now substituted by Lemma 2.5, which contains an extra hypothesis, added also to Proposition 2.7. The other results are essentially unchanged (it is now checked that the examples satisfy the extra hypothesis). To appear in OJM