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2017 On Abelian Canonical $n$-folds of General Type
Rong Du, Yun Gao
Taiwanese J. Math. 21(3): 653-664 (2017). DOI: 10.11650/tjm/7915


Let $X$ be a Gorenstein minimal projective $n$-fold with at worst locally factorial terminal singularities, and suppose that the canonical map of $X$ is generically finite onto its image. When $n \lt 4$, the canonical degree is universally bounded. While the possibility of obtaining a universal bound on the canonical degree of $X$ for $n \geq 4$ may be inaccessible, we give a uniform upper bound for the degrees of certain abelian covers. In particular, we show that if the canonical divisor $K_X$ defines an abelian cover over $\mathbb{P}^n$, i.e., when $X$ is an abelian canonical $n$-fold, then the canonical degree of $X$ is universally upper bounded by a constant which only depends on $n$ for $X$ nonsingular. We also construct two examples of nonsingular minimal projective $4$-folds of general type with canonical degrees $81$ and $128$.


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Rong Du. Yun Gao. "On Abelian Canonical $n$-folds of General Type." Taiwanese J. Math. 21 (3) 653 - 664, 2017.


Published: 2017
First available in Project Euclid: 1 July 2017

zbMATH: 06871336
MathSciNet: MR3661385
Digital Object Identifier: 10.11650/tjm/7915

Primary: 14E20 , 14J35 , 14J40

Keywords: abelian canonical $n$-fold , abelian cover , canonical degree , Canonical map

Rights: Copyright © 2017 The Mathematical Society of the Republic of China


Vol.21 • No. 3 • 2017
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