Effective Bounds of Linear Series on Algebraic Varieties and Arithmetic Varieties
classification
🧮 math.NT
math.AG
keywords
effectivevarietiesarithmeticboundsbundlesformulahilbert--samuelline
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In this paper, we prove effective upper bounds for effective sections of line bundles on projective varieties and hermitian line bundles on arithmetic varieties in terms of the volumes. They are effective versions of the Hilbert--Samuel formula and the arithmetic Hilbert--Samuel formula.
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