Weyl and Zariski chambers on K3 surfaces

Abstract

The big cone of every K3 surface admits two natural chamber decompositions: the decomposition into Zariski chambers, and the decomposition into simple Weyl chambers. In the present paper we compare these two decompositions and we study their mutual relationship: First, we give a numerical criterion for the two decompositions to coincide. Secondly, we study the mutual inclusions of Zariski and simple Weyl chambers. Finally, we establish the fact that -- even though the decompositions themselves may differ -- the number of Zariski chambers always equals the number of simple Weyl chambers.