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Log Fano structures and Cox rings of blow-ups of products of projective spaces


Authors: John Lesieutre and Jinhyung Park
Journal: Proc. Amer. Math. Soc. 145 (2017), 4201-4209
MSC (2010): Primary 14J45; Secondary 14E30, 14C20
DOI: https://doi.org/10.1090/proc/13610
Published electronically: April 7, 2017
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Abstract: The aim of this paper is twofold. First, we determine which blow-ups of products of projective spaces at general points are varieties of Fano type, and give boundary divisors making these spaces log Fano pairs. Second, we describe generators of the Cox rings of some cases.


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Additional Information

John Lesieutre
Affiliation: Department of Mathematics, University of Illinois at Chicago, 851 South Morgan Street, Chicago, Illinois 60607
Email: jdl@uic.edu

Jinhyung Park
Affiliation: School of Mathematics, Korea Institute for Advanced Study, 85 Hoegiro, Dongdaemungu, Seoul 02455, Republic of Korea
Email: parkjh13@kias.re.kr

DOI: https://doi.org/10.1090/proc/13610
Keywords: log Fano variety, Cox ring, Mori dream space, blow-up of a product of projective spaces
Received by editor(s): May 4, 2016
Received by editor(s) in revised form: November 3, 2016
Published electronically: April 7, 2017
Communicated by: Lev Borisov
Article copyright: © Copyright 2017 American Mathematical Society

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