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Small bound for birational automorphism groups of algebraic varieties (with an Appendix by Yujiro Kawamata)

De-Qi Zhang
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Abstract

We give an effective upper bound of |Bir(X)| for the birational automorphism group of an irregular n-fold (with n = 3) of general type in terms of the volume V = V(X) under an ''albanese smoothness and simplicity'' condition. To be precise, |Bir(X)| < d_3 V^{10}. An optimum linear bound |Bir(X)|-1 < (1/3)(42)^3 V is obtained for those 3-folds with non-maximal albanese dimension. For all n > 2, a bound |Bir(X)| < d_n V^{10} is obtained when alb_X is generically finite, alb(X) is smooth and Alb(X) is simple.

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De-Qi Zhang. 2006-09-04. Small bound for birational automorphism groups of algebraic varieties (with an Appendix by Yujiro Kawamata). https://arxiv.org/abs/math/0609083

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