scholarly journals Periodic subvarieties of a projective variety under the action of a maximal rank abelian group of positive entropy

2018 ◽  
Vol 22 (3) ◽  
pp. 451-476
Author(s):  
Fei Hu ◽  
Sheng-Li Tan ◽  
De-Qi Zhang
Keyword(s):  
Abelian Group ◽  
Projective Variety ◽  
Maximal Rank ◽  
Positive Entropy

scholarly journals Free abelian group actions on normal projective varieties: submaximal dynamical rank case

2020 ◽  
pp. 1-17
Author(s):  
Fei Hu ◽  
Sichen Li
Keyword(s):  
Abelian Group ◽  
Projective Variety ◽  
Free Abelian Group ◽  
Group Actions ◽  
Maximal Rank ◽  
Positive Entropy ◽  
Projective Varieties ◽  
Group Of Automorphisms ◽  
Abelian Group Actions ◽  
De Qi

Abstract Let X be a normal projective variety of dimension n and G an abelian group of automorphisms such that all elements of $G\setminus \{\operatorname {id}\}$ are of positive entropy. Dinh and Sibony showed that G is actually free abelian of rank $\le n - 1$ . The maximal rank case has been well understood by De-Qi Zhang. We aim to characterize the pair $(X, G)$ such that $\operatorname {rank} G = n - 2$ .

group shifts and Bernoulli factors

2008 ◽  
Vol 28 (2) ◽  
pp. 367-387 ◽  
Author(s):  
MIKE BOYLE ◽  
MICHAEL SCHRAUDNER
Keyword(s):  
Abelian Group ◽  
Bernoulli Shift ◽  
Continuous Group ◽  
Positive Entropy ◽  
Completely Positive ◽  
Bernoulli Shifts ◽  
Dimensional Group ◽  
Vector Shift ◽  
Group Shift

AbstractIn this paper, a group shift is an expansive action of $\Z ^d$ on a compact metrizable zero-dimensional group by continuous automorphisms. All group shifts factor topologically onto equal-entropy Bernoulli shifts; abelian group shifts factor by continuous group homomorphisms onto canonical equal-entropy Bernoulli group shifts; and completely positive entropy abelian group shifts are weakly algebraically equivalent to these Bernoulli factors. A completely positive entropy group (even vector) shift need not be topologically conjugate to a Bernoulli shift, and the Pinsker factor of a vector shift need not split topologically.

Model sets with positive entropy in Euclidean cut and project schemes

2019 ◽  
Vol 52 (5) ◽  
pp. 1073-1106 ◽  
Author(s):  
Tobias JÄGER ◽  
Daniel LENZ ◽  
Christian OERTEL
Keyword(s):  
Positive Entropy ◽  
Model Sets

Maximal rank divisors on M_g,n

2020 ◽  
Vol 20 (1) ◽  
pp. 349-371
Author(s):  
İrfan Kadiköylü
Keyword(s):  
Maximal Rank
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