Paper detail

Compactifications of affine homology $3$-cells into blow-ups of the projective $3$-space with trivial log canonical divisors

In this paper we classify all the compactifications of affine homology $3$-cells into the blow-ups of the projective $3$-space along smooth curves such that the log canonical divisors are linearly trivial. As a result, we prove that each embedded affine $3$-fold is isomorphic to the affine $3$-space except one example.