Abstract
We compute the facets of the effective cones of divisors on the blow-up of \({\mathbb {P}}^3\) in up to five lines in general position. We prove that up to six lines these threefolds are weak Fano and hence Mori Dream Spaces.
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Acknowledgements
The authors would like to thank the organizers of the workshop “Recent advances in Linear series and Newton–Okounkov bodies”, Università degli Studi di Padova, 2015, for their hospitality and financial support. This collaboration and project was started there. We would also like to thank M. Bolognesi and M. C. Brambilla for helpful conversations. We thank the referee for useful comments and suggestions on the first version of this manuscript.
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The first author is a member of the Simion Stoilow Institute of Mathematics of the Romanian Academy. The second author is supported by the Research Foundation—Flanders (FWO). The third author is supported by the PISCOPIA cofund Marie Curie Fellowship Programme.
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Dumitrescu, O., Postinghel, E. & Urbinati, S. Cones of effective divisors on the blown-up \({\mathbb {P}}^3\) in general lines. Rend. Circ. Mat. Palermo, II. Ser 66, 205–216 (2017). https://doi.org/10.1007/s12215-016-0280-8
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DOI: https://doi.org/10.1007/s12215-016-0280-8