Normal crossings singularities for symplectic topology
| Autor: | Mark McLean, Aleksey Zinger, Mohammad Farajzadeh Tehrani |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Pure mathematics
Logarithm Divisor General Mathematics 010102 general mathematics 01 natural sciences Mathematics - Algebraic Geometry Mathematics - Symplectic Geometry 0103 physical sciences FOS: Mathematics Symplectic Geometry (math.SG) 53D05 53D45 14N35 Gravitational singularity 010307 mathematical physics 0101 mathematics Equivalence (formal languages) Algebraic Geometry (math.AG) Mathematics::Symplectic Geometry Symplectic sum Symplectic geometry Mathematics |
| Zdroj: | Advances in Mathematics. 339:672-748 |
| ISSN: | 0001-8708 |
| DOI: | 10.1016/j.aim.2018.09.035 |
| Popis: | We introduce topological notions of normal crossings symplectic divisor and variety and establish that they are equivalent, in a suitable sense, to the desired geometric notions. Our proposed concept of equivalence of associated topological and geometric notions fits ideally with important constructions in symplectic topology. This partially answers Gromov's question on the feasibility of defining singular symplectic (sub)varieties and lays foundation for rich developments in the future. In subsequent papers, we establish a smoothability criterion for symplectic normal crossings varieties, in the process providing the multifold symplectic sum envisioned by Gromov, and introduce symplectic analogues of logarithmic structures in the context of normal crossings symplectic divisors. Comment: 65 pages, 4 figures; a number of typos fixed; the exposition has been significantly revised, fixing a technical error in the non-compact case in the process; this paper is now restricted to the simple normal crossings case; the arbitrary normal crossings case will be detailed in a followup paper |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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