Abstract.
The change of zero locus of a global holomorphic 2-form on a threefold under birational transformations is investigated. It is proved that existence of 2-forms with certain conditions on their zero loci on a threefold of nonnegative Kodaira dimension limits types of terminal singularities appearing on its minimal models. As a result of the restriction on the types of terminal singularities and Reid's Riemann-Roch formula, a universal bound N is found such that the linear system NK defines a birational map from a threefold of general type admitting those 2-forms, where K is the canonical bundle of the threefold.
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Received March 10, 2000 / Published online October 11, 2000
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Luo, T. Global holomorphic 2-forms and pluricanonical systems on threefolds. Math Ann 318, 707–730 (2000). https://doi.org/10.1007/s002080000136
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DOI: https://doi.org/10.1007/s002080000136