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arXiv · 2007.06519

An integral version of Zariski decompositions on normal surfaces

Makoto Enokizono
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Abstract

We show that any pseudo-effective divisor on a normal surface decomposes uniquely into its "integral positive" part and "integral negative" part, which is an integral analog of Zariski decompositions. By using this decomposition, we give three applications: a vanishing theorem of divisors on surfaces (a generalization of Kawamata-Viehweg and Miyaoka vanishing theorems), Reider-type theorems of adjoint linear systems on surfaces (including a log version and a relative version of the original one) and extension theorems of morphisms defined on curves on surfaces (generalizations of Serrano and Paoletti's results).

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Makoto Enokizono. 2020-07-13. An integral version of Zariski decompositions on normal surfaces. https://arxiv.org/abs/2007.06519

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