Zariski's conjecture and Euler-Chow series
| Autor: | Chen, Xi, Elizondo, E. javier |
|---|---|
| Rok vydání: | 2019 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | We study the relations between the finite generation of Cox ring, the rationality of Euler-Chow series and Poincar\'e 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 Poincar\'e series of the variety are rational. We also prove that the multi-variable Poincar\'e series associated to big divisors on a smooth projective surface are rational, assuming the rationality of multi-variable Poincare series on curves. Comment: 24 pages. To appear in Bolet\'in de la Sociedad Matem\'atica Mexicana |
| Databáze: | arXiv |
| Externí odkaz: |
|