Abstract
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.
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Acknowledgements
The author thanks greatly to Zhi Jiang who, besides giving this problem, pointed out several significant mistakes in the original draft of this paper and made a variety of useful suggestions. This research work is supported by the National Key R and D Program of China 2020YFA0713100, National Natural Science Foundation of China (Grant No. 11721101), the Fundamental Research Funds for the Central Universities (No. WK3470000018) and Anhui Initiative in Quantum Information Technologies (AHY150200).
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Chen, Y. Generic finiteness of 3-canonical maps of varieties of Albanese fiber dimension one. Collect. Math. 74, 547–565 (2023). https://doi.org/10.1007/s13348-022-00364-7
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DOI: https://doi.org/10.1007/s13348-022-00364-7