graded linear series
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2021 ◽  
Author(s):  
Chih-Wei Chang ◽  
Shin-Yao Jow


2019 ◽  
Vol 6 (2) ◽  
pp. 367-399
Author(s):  
Huayi Chen ◽  
Hideaki Ikoma


Author(s):  
Tomoyuki Hisamoto

AbstractWe apply our integral formula of volumes to the family of graded linear series constructed from any test configuration. This solves the conjecture raised by Witt Nyström to the effect that the sequence of spectral measures for the induced ℂ



2012 ◽  
Vol 275 (1-2) ◽  
pp. 233-243 ◽  
Author(s):  
Tomoyuki Hisamoto


2011 ◽  
Vol 147 (4) ◽  
pp. 1205-1229 ◽  
Author(s):  
Sébastien Boucksom ◽  
Huayi Chen

AbstractWe associate to certain filtrations of a graded linear series of a big line bundle a concave function on its Okounkov body, whose law with respect to the Lebesgue measure describes the asymptotic distribution of the jumps of the filtration. As a consequence, we obtain a Fujita-type approximation theorem in this general filtered setting. We then specialize these results to the filtrations by minima in the usual context of Arakelov geometry (and for more general adelically normed graded linear series), thereby obtaining in a simple way a natural construction of an arithmetic Okounkov body, the existence of the arithmetic volume as a limit and an arithmetic Fujita approximation theorem for adelically normed graded linear series. We also obtain an easy proof of the existence of the sectional capacity previously obtained by Lau, Rumely and Varley.



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