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The zeroth line bundle cohomology on Calabi-Yau three-folds encodes information about the existence of flop transitions and the genus zero Gromov-Witten invariants.
1906
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Zariski-decomposition and Abundance
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R. Lazarsfeld, Positivity in Algebraic Geometry I: Classical Setting: Line Bundles and Linear Series · 2004
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P. Wilson, “Boundedness questions for Calabi-Yau threefolds,” 1706.01268v4
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