scholarly journals Compact Kähler threefolds with the action of an abelian group of maximal rank

2021 ◽  
pp. 1
Author(s):  
Guolei Zhong
Keyword(s):  
Abelian Group ◽  
Maximal Rank

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 $\operatorname {rank} G = n - 2$ .

Maximal rank divisors on M_g,n

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

Additive bases via Fourier analysis

2021 ◽  
pp. 1-12
Author(s):  
Bodan Arsovski
Keyword(s):  
Abelian Group ◽  
Fourier Analysis ◽  
Vector Space ◽  
Abelian Groups ◽  
Finite Abelian Group ◽  
Probabilistic Method ◽  
Additive Basis ◽  
Generating Sets

Abstract Extending a result by Alon, Linial, and Meshulam to abelian groups, we prove that if G is a finite abelian group of exponent m and S is a sequence of elements of G such that any subsequence of S consisting of at least $$|S| - m\ln |G|$$ elements generates G, then S is an additive basis of G . We also prove that the additive span of any l generating sets of G contains a coset of a subgroup of size at least $$|G{|^{1 - c{ \in ^l}}}$$ for certain c=c(m) and $$ \in = \in (m) < 1$$ ; we use the probabilistic method to give sharper values of c(m) and $$ \in (m)$$ in the case when G is a vector space; and we give new proofs of related known results.

scholarly journals CONTINUITY OF MEASURABLE HOMOMORPHISMS

2008 ◽  
Vol 78 (1) ◽  
pp. 171-176 ◽  
Author(s):  
JANUSZ BRZDȨK
Keyword(s):  
Topological Group ◽  
Abelian Group ◽  
Baire Property ◽  
Topological Groups ◽  
Locally Compact ◽  
Compact Topological Group ◽  
Locally Compact Topological Group

AbstractWe give some general results concerning continuity of measurable homomorphisms of topological groups. As a consequence we show that a Christensen measurable homomorphism of a Polish abelian group into a locally compact topological group is continuous. We also obtain similar results for the universally measurable homomorphisms and the homomorphisms that have the Baire property.

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