Please use this identifier to cite or link to this item: https://doi.org/10.1090/tran/6629
Title: n-DIMENSIONAL PROJECTIVE VARIETIES WITH THE ACTION OF AN ABELIAN GROUP OF RANK n-1
Authors: Zhang, De-Qi 
Keywords: Science & Technology
Physical Sciences
Mathematics
Automorphism
iteration
complex dynamics
tori
topological entropy
COMPACT KAHLER-MANIFOLDS
AUTOMORPHISM-GROUPS
Issue Date: 1-Dec-2016
Publisher: AMER MATHEMATICAL SOC
Citation: Zhang, De-Qi (2016-12-01). n-DIMENSIONAL PROJECTIVE VARIETIES WITH THE ACTION OF AN ABELIAN GROUP OF RANK n-1. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY 368 (12) : 8849-8872. ScholarBank@NUS Repository. https://doi.org/10.1090/tran/6629
Abstract: Let X be a normal projective variety of dimension n ≥ 3 admitting the action of the group G:= ℤ⊕n−1 such that every non-trivial element of G is of positive entropy. We show: ‘X is not rationally connected’ ⇒ ‘X is Gequivariant birational to the quotient of a complex torus’ ⇐⇒ ‘KX + D is pseudo-effective for some G-periodic effective fractional divisor D’. To apply, one uses the above and the fact: ‘the Kodaira dimension κ(X) ≥ 0’ ⇒ ‘X is not uniruled’ ⇒ ‘X is not rationally connected’. We may generalize the result to the case of solvable G.
Source Title: TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
URI: https://scholarbank.nus.edu.sg/handle/10635/234642
ISSN: 0002-9947
1088-6850
DOI: 10.1090/tran/6629
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