scholarly journals Finite generation of the log canonical ring in dimension four

2010 ◽  
Vol 50 (4) ◽  
pp. 671-684 ◽  
Author(s):  
Osamu Fujino
Keyword(s):  
Finite Generation ◽  
Log Canonical ◽  
Canonical Ring

scholarly journals On the semiampleness of the positive part of CKM Zariski decompositions

2013 ◽  
Vol 156 (1) ◽  
pp. 1-23 ◽  
Author(s):  
SALVATORE CACCIOLA
Keyword(s):  
Graded Rings ◽  
Positive Part ◽  
Finite Generation ◽  
Canonical Divisor ◽  
Log Canonical

AbstractWe study graded rings associated to big divisors on LC pairs whose difference with the log-canonical divisor is nef. For divisors that are positive enough at the LC centers of the pair, we prove the finite generation of such rings if the pair is DLT or the dimension is low, given that a Zariski decomposition exists.

scholarly journals On the log canonical ring with Kodaira dimension two

2020 ◽  
pp. 2050121
Author(s):  
Haidong Liu
Keyword(s):  
Kodaira Dimension ◽  
Finitely Generated ◽  
Log Canonical ◽  
Canonical Pair ◽  
Canonical Ring

We prove that the log canonical ring of a projective log canonical pair with Kodaira dimension two is finitely generated.

scholarly journals Non-branching RCD(0,N) Geodesic Spaces with Small Linear Diameter Growth have Finitely Generated Fundamental Groups

2015 ◽  
Vol 58 (4) ◽  
pp. 787-798 ◽  
Author(s):  
Yu Kitabeppu ◽  
Sajjad Lakzian
Keyword(s):  
Diameter Growth ◽  
Fundamental Groups ◽  
Finitely Generated ◽  
Finite Generation ◽  
Alexandrov Spaces ◽  
Geodesic Spaces ◽  
Special Case ◽  
Linear Diameter

AbstractIn this paper, we generalize the finite generation result of Sormani to non-branching RCD(0, N) geodesic spaces (and in particular, Alexandrov spaces) with full supportmeasures. This is a special case of the Milnor’s Conjecture for complete non-compact RCD(0, N) spaces. One of the key tools we use is the Abresch–Gromoll type excess estimates for non-smooth spaces obtained by Gigli–Mosconi.

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