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Nowhere vanishing 1-forms on varieties admitting a good minimal model
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We prove several conjectures relating the existence of nonvanishing 1- forms to smooth morphisms over abelian varieties, assuming the existence of good minimal models. The proof involves a decomposition result for a family of Calabi-Yau varieties equipped with a surjective map to an abelian scheme. In the uniruled case, supposing the MRC base admits a good minimal model, we also achieve a structure theorem for those varieties admitting nowhere vanishing 1-forms.
Forward citations
Cited by 2 Pith papers
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Invisible singularities in complex algebraic geometry
Morphisms from smooth projective varieties to P^1 can have singular fibers that are topologically invisible, yielding counterexamples to the Fernandez de Bobadilla-Kollar, Kollar-Pardon, Kotschick, and Schreieder conjectures.
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Zeros of one-forms and the topology of algebraic maps
New explicit projective varieties disprove Kotschick's conjecture, the remaining implication of the Bobadilla–Kollár conjecture, and Schreieder's conjecture on zeros of holomorphic one-forms.
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