Generic finiteness of 3-canonical maps of varieties of Albanese fiber dimension one

Chen, Yuesen ^[1]
1. [1] University of Science and Technology of China
  
  University of Science and Technology of China
  
  China
Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 74, Fasc. 3, 2023, págs. 547-565
Idioma: inglés
DOI: 10.1007/s13348-022-00364-7
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Resumen
- We prove that for a variety of Albanese fiber dimension one and of general type, the generic twisted 3-canonical map is generically finite, under which the Albanese morphism is an isogeny. As an application, we also show that for such varieties with dimensional three and large volume, the degree of twisted 3-canonical maps are at most 2, which leads to a generic birationality property on itself.