When are Zariski chambers numerically determined?
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Sławomir Rams
Abstract
The big cone of every smooth projective surface X admits a natural decomposition into Zariski chambers. The purpose of this note is to give a simple criterion for the interiors of all Zariski chambers on X to be numerically determined Weyl chambers. Such a criterion generalizes the results of Bauer–Funke [4] on K3 surfaces to arbitrary smooth projective surfaces. In the last section, we study the relation between decompositions of the big cone and elliptic fibrations on some surfaces.
Funding source: Narodowe Centrum Nauki
Award Identifier / Grant number: N N201 608040
Award Identifier / Grant number: 2014/15/B/ST1/02197
Funding statement: The work was partially supported by National Science Centre, Poland, grant no. N N201 608040 (first author) and grant no. 2014/15/B/ST1/02197 (second author).
Acknowledgements
The first author would like to thank T. Bauer, M. Joumaah and M. Schütt for useful discussions. We thank I. Dolgachev for answering our questions on the r-invariant of Enriques surfaces and anonymous referees for their inspiring remarks (in particular, for the idea of the proof of Lemma 14).
References
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- When are Zariski chambers numerically determined?
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Articles in the same Issue
- Frontmatter
- Behavior of bounds of singular integrals for large dimension
- The twofold way of super holonomy
- On mod p singular modular forms
- Martin boundary of unbounded sets for purely discontinuous Feller processes
- Bi-parameter and bilinear Calderón–Vaillancourt theorem with subcritical order
- Nontrivial solutions of superlinear nonlocal problems
- Hopfian $\ell$-groups, MV-algebras and AF~{C}*-algebras
- On regularization of vector distributions on manifolds
- The Addition Theorem for algebraic entropies induced by non-discrete length functions
- When are Zariski chambers numerically determined?
- Convexity theorems for semisimple symmetric spaces
- On amenability of groups generated by homogeneous automorphisms and their cracks
