Non-Affine Stein Manifolds and Normal Crossing Divisors

Abstract

We show that there are Stein manifolds that admit normal crossing divisor compactifications despite being neither affine nor quasi-projective. To achieve this, we study the contact boundaries of neighborhoods of symplectic normal crossing divisors via a contact-geometric analog of W. Neumann's plumbing calculus. In particular, we give conditions under which the neighborhood is determined by the contact structure on its boundary.