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.
Nowhere vanishing 1-forms on varieties admitting a good minimal model
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
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.
fields
math.AG 1years
2026 1verdicts
ACCEPT 1representative citing papers
citing papers explorer
-
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.