Dimca Hypersurfaces and Nagata Automorphisms

Abstract

Choudary–Dimca [CD ] proved that Dimca hypersurfaces are diffeomorphic to ℝ2n and some of the hypersurfaces with dimension 3 are isomorphic to the plane and the embeddings are equivalent to linear embeddings. However, neither an isomorphism nor a trivializing polynomial automorphism was given explicitly. The purpose of the present paper is to give these explicitly.

Singular Fano compactifications of (I)

“…Then the affine part B * := B ∩ {x 3 = 0} is isomorphic to C 2 and there is an algebraic automorphism θ ∈ Aut C 3 such that θ(B * ) is a linear plane in C 3 (see [37]). Let ϕ : V 2 −→ P 3 be the double cover of P 3 branched along B.…”