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Cox rings of extremal rational elliptic surfaces


Authors: Michela Artebani, Alice Garbagnati and Antonio Laface
Journal: Trans. Amer. Math. Soc. 368 (2016), 1735-1757
MSC (2010): Primary 14J26, 14C20
DOI: https://doi.org/10.1090/tran/6378
Published electronically: July 10, 2015
MathSciNet review: 3449224
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Abstract: In this paper we determine a minimal set of generators for the Cox rings of extremal rational elliptic surfaces. Moreover, we develop a technique for computing the ideal of relations between them which allows us to provide a presentation of the Cox ring in most cases.


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Additional Information

Michela Artebani
Affiliation: Departamento de Matemática, Universidad de Concepción, Casilla 160-C, Concepción, Chile
Email: martebani@udec.cl

Alice Garbagnati
Affiliation: Dipartimento di Matematica, Università Statale degli Studi di Milano via Saldini, 50, I-20133 Milano, Italy
Email: alice.garbagnati@unimi.it

Antonio Laface
Affiliation: Departamento de Matemática, Universidad de Concepción, Casilla 160-C, Concepción, Chile
Email: alaface@udec.cl

DOI: https://doi.org/10.1090/tran/6378
Keywords: Cox rings, rational elliptic surfaces
Received by editor(s): May 1, 2013
Received by editor(s) in revised form: January 1, 2014
Published electronically: July 10, 2015
Additional Notes: The first author was partially supported by Proyecto FONDECYT Regular N. 1110249 and N. 1130572. The second author was partially supported by PRIN 2010-2011 “Geometria delle varietà algebriche” and FIRB 2012 “Moduli Spaces and their Applications”. The third author was partially supported by Proyecto FONDECYT regular N. 1110096 and N. 1150732
Article copyright: © Copyright 2015 American Mathematical Society