On pluricanonical boundedness of varieties of general type
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918144694550528 |
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| author | Wang, Pengjin |
| author_facet | Wang, Pengjin |
| contents | We present a new proof of a theorem of Chen and Jiang: for any integer $n>1$, there is a constant $K_n>0$ such that every smooth projective $n$-fold $X$ with $\operatorname{vol}(X)>K_n$ has either the stable birational $2$-canonical map or a M$^c$Kernan fibration. This amends a gap in the original proof. As a direct application of our method, we improve a former boundedness theorem of Lacini and prove that for any integer $r>1$ and $n\geq 1$, $r$-canonical maps of $n$-folds of general type have birationally bounded fibers. This gives an affirmative answer to a question posed by Chen and Jiang in 2014. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_21459 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On pluricanonical boundedness of varieties of general type Wang, Pengjin Algebraic Geometry 14E05, 14J30, 14J35, 14J40 We present a new proof of a theorem of Chen and Jiang: for any integer $n>1$, there is a constant $K_n>0$ such that every smooth projective $n$-fold $X$ with $\operatorname{vol}(X)>K_n$ has either the stable birational $2$-canonical map or a M$^c$Kernan fibration. This amends a gap in the original proof. As a direct application of our method, we improve a former boundedness theorem of Lacini and prove that for any integer $r>1$ and $n\geq 1$, $r$-canonical maps of $n$-folds of general type have birationally bounded fibers. This gives an affirmative answer to a question posed by Chen and Jiang in 2014. |
| title | On pluricanonical boundedness of varieties of general type |
| topic | Algebraic Geometry 14E05, 14J30, 14J35, 14J40 |
| url | https://arxiv.org/abs/2508.21459 |