2025/12/07 by Masuda, Kayo
Mathematics · #Algebraic Geometry and Number Theory #Geometry and complex manifolds #Advanced Algebra and Geometry
paper · doi:10.48550/arxiv.2512.06687
Let X be a factorial complex affine variety of dimension ≥ 3 with an algebraic action of the additive group Ga. Let π: X → Y be the algebraic quotient morphism where we assume Y is an affine variety. When π is faithfully flat, we investigate π by Ga-equivariant affine modifications and give criteria for π to be a trivial \mathbb A1-bundle. For a smooth acyclic fourfold X with a free Ga-action and a Ga-equivariant \mathbb A3-fibration f : X → \mathbb A1 where Ga acts trivially on \mathbb A1, we give a criterion for the algebraic quotient Y to be isomorphic to \mathbb A3 with f as a coordinate. Together with a criterion for π: X → Y to be a trivial \mathbb A1-bundle, we obtain a sufficient condition for X≅ Y× \mathbb A1≅ \mathbb A4.