Abstract
Let X be a nonsingular complex projective surface. The Weyl and Zariski chambers give two interesting decompositions of the big cone of X. Following the ideas of [T. Bauer and M. Funke, Weyl and Zariski chambers on K3 surfaces, Forum Math. 24 2012, 3, 609–625] and [S. A. Rams and T. Szemberg, When are Zariski chambers numerically determined?, Forum Math. 28 2016, 6, 1159–1166], we study these two decompositions and determine when a Weyl chamber is contained in the interior of a Zariski chamber and vice versa. We also determine when a Weyl chamber can intersect non-trivially with a Zariski chamber.
Funding statement: First author was partially supported by a grant from Infosys Foundation and by DST SERB MATRICS grant MTR/2017/000243.
Acknowledgements
Part of this work was done when the first author visited the Tata Institute of Fundamental Research, Mumbai. He is grateful for the hospitality.
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