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Zariski’s conjecture and Euler–Chow series
We study the relations between the finite generation of Cox ring, the rationality of Euler–Chow series and Poincaré series and Zariski’s conjecture on dimensions of linear systems. We prove that if the Cox ring of a smooth projective variety is finitely generated, then all Poincaré series of the var...
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Published in: | Boletín de la Sociedad Matemática Mexicana 2020-11, Vol.26 (3), p.921-946 |
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Main Authors: | , |
Format: | Article |
Language: | English |
Subjects: | |
Citations: | Items that this one cites |
Online Access: | Get full text |
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Summary: | We study the relations between the finite generation of Cox ring, the rationality of Euler–Chow series and Poincaré series and Zariski’s conjecture on dimensions of linear systems. We prove that if the Cox ring of a smooth projective variety is finitely generated, then all Poincaré series of the variety are rational. We also prove that the multi-variable Poincaré series associated to big divisors on a smooth projective surface are rational, assuming the rationality of multi-variable Poincaré series on curves. |
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ISSN: | 1405-213X 2296-4495 |
DOI: | 10.1007/s40590-020-00285-0 |