On compactifications of affine homology 3-cells into quadric fibrations

Abstract

In this paper we deal with compactifications of affine homology $3$-cells into quadric fibrations such that the boundary divisors contain fibers. We show that all such affine homology $3$-cells are isomorphic to the affine $3$-space ${\mathbb{A}}^3$. Moreover, we show that all such compactifications can be connected by explicit elementary links preserving ${\mathbb{A}}^3$ to the projective $3$-space ${\mathbb{P}}^3$.

25 pages, 1 figure; modified the statement of the main problem

References in corpus (1)

• Relative linear extensions of sextic del Pezzo fibrations

Cited by in corpus (2)

• ${\mathbb{G}}_a^3$-structures on del Pezzo fibrations
• Compactifications of affine homology $3$-cells into blow-ups of the projective $3$-space with trivial log canonical divisors