ON THE VOLUME OF A LINE BUNDLE
2002 ◽
Vol 13
(10)
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pp. 1043-1063
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Keyword(s):
The Mean
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Using the Calabi–Yau technique to solve Monge-Ampère equations, we translate a result of T. Fujita on approximate Zariski decompositions into an analytic setting and combine this to the holomorphic Morse inequalities in order to express the volume of a line bundle as the maximum of the mean curvatures of all the singular Hermitian metrics on it, with a way to pick an element at which the maximum is reached and satisfying a singular Monge–Ampère equation. This enables us to introduce the volume of any (1,1)-class on a compact Kähler manifold, and Fujita's theorem is then extended to this context.
Keyword(s):
2014 ◽
Vol 150
(11)
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pp. 1869-1902
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Keyword(s):
Keyword(s):
2016 ◽
Vol 30
(2)
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pp. 311-346
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Keyword(s):
1978 ◽
Vol 31
(3)
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pp. 339-411
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Keyword(s):
2006 ◽
Vol 17
(01)
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pp. 35-43
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1995 ◽
Vol 10
(30)
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pp. 4325-4357
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2012 ◽
Vol 22
(2)
◽
pp. 201-248
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