Nowhere vanishing 1-forms on varieties admitting a good minimal model
Benjamin Church

TL;DR
This paper proves conjectures linking nonvanishing 1-forms on varieties with good minimal models, revealing structural properties and decompositions involving Calabi-Yau and uniruled varieties over abelian schemes.
Contribution
It establishes new connections between nonvanishing 1-forms and smooth morphisms, and provides a structure theorem for certain varieties assuming minimal model existence.
Findings
Proved conjectures relating 1-forms to morphisms over abelian varieties.
Decomposition result for families of Calabi-Yau varieties with surjective maps.
Structure theorem for uniruled varieties with nowhere vanishing 1-forms.
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.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Numerical Analysis Techniques · Polynomial and algebraic computation
