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On birational maps from cubic threefolds

Blanc, Jérémy and Lamy, Stéphane. (2015) On birational maps from cubic threefolds. North-Western European Journal of Mathematics, Vol. 1. S. 55-84.

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Official URL: http://edoc.unibas.ch/dok/A6428786

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Abstract

We characterise smooth curves in a smooth cubic threefold whose blow-ups produce a weak-Fano threefold. These are curves C of genus g and degree d, such that (i) 2(d −5) ≤ g and d ≤ 6; (ii) C does not admit a 3-secant line in the cubic threefold. Among the list of ten possible such types (g,d), two yield Sarkisov links that are birational selfmaps of the cubic threefold, namely (g,d) = (0,5) and (2,6). Using the link associated with a curve of type (2, 6), we are able to produce the first example of a pseudo-automorphism with dynamical degree greater than 1 on a smooth threefold with Picard number 3. We also prove that the group of birational selfmaps of any smooth cubic threefold contains elements contracting surfaces birational to any given ruled surface.
Faculties and Departments:05 Faculty of Science > Departement Mathematik und Informatik > Mathematik > Algebra (Blanc)
UniBasel Contributors:Blanc, Jérémy
Item Type:Article, refereed
Bibsysno:Link to catalogue
Note:Publication type according to Uni Basel Research Database: Journal article
Last Modified:02 Oct 2015 10:00
Deposited On:02 Oct 2015 10:00

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