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• W2238404744 abstract "We introduce a Zariski decomposition for curve classes and use it to develop the theory of the volume function for curves defined by the second named author. For toric varieties and for hyperkahler manifolds the Zariski decomposition admits an interesting geometric interpretation. With the decomposition, we prove some fundamental positivity results for curve classes, such as a Morse-type inequality. We compare the volume of a curve class with its mobility, yielding some surprising results about asymptotic point counts. Finally, we give a number of applications to birational geometry, including a refined structure theorem for the movable cone of curves." @default.
• W2238404744 created "2016-06-24" @default.
• W2238404744 creator A5056331639 @default.
• W2238404744 creator A5072853514 @default.
• W2238404744 date "2015-07-15" @default.
• W2238404744 modified "2023-10-05" @default.
• W2238404744 title "Zariski decomposition of curves on algebraic varieties" @default.
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• W2238404744 hasPublicationYear "2015" @default.
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