Non-Affine Stein Manifolds and Normal Crossing Divisors
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918107604320256 |
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| author | Van Why, Randall R. |
| author_facet | Van Why, Randall R. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_22290 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Non-Affine Stein Manifolds and Normal Crossing Divisors Van Why, Randall R. Symplectic Geometry Algebraic Geometry Complex Variables 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. |
| title | Non-Affine Stein Manifolds and Normal Crossing Divisors |
| topic | Symplectic Geometry Algebraic Geometry Complex Variables |
| url | https://arxiv.org/abs/2507.22290 |