Small bound for birational automorphism groups of algebraic varieties (with an Appendix by Yujiro Kawamata)
Algebraic Geometry
2018-09-24 v1
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.
Keywords
Cite
@article{arxiv.math/0609083,
title = {Small bound for birational automorphism groups of algebraic varieties (with an Appendix by Yujiro Kawamata)},
author = {De-Qi Zhang},
journal= {arXiv preprint arXiv:math/0609083},
year = {2018}
}
Comments
Mathematische Annalen, to appear