On integral Zariski decompositions of pseudoeffective divisors on algebraic surfaces
classification
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decompositionszariskialgebraiccurvesdivisorsintegralintegralitypseudoeffective
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In this note we consider the problem of integrality of Zariski decompositions for pseudoeffective integral divisors on algebraic surfaces. We show that while sometimes integrality of Zariski decompositions forces all negative curves to be $(-1)$-curves, there are examples where this is not true.
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