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Topological invariance of intersection lattices of arrangements in $ \mathbf{CP}^2$


Authors: Tan Jiang and Stephen S.-T. Yau
Journal: Bull. Amer. Math. Soc. 29 (1993), 88-93
MSC (2000): Primary 52B30; Secondary 32S50, 57N10
DOI: https://doi.org/10.1090/S0273-0979-1993-00409-9
MathSciNet review: 1197426
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Abstract: Let $ {\mathcal{A}^{\ast}} = \{ {l_{1}},{l_{2}},...,{l_n}\} $ be a line arrangement in $ \mathbb{C}{\mathbb{P}^2}$, i.e., a collection of distinct lines in $ \mathbb{C}{\mathbb{P}^2}$. Let $ L({\mathcal{A}^{\ast}})$ be the set of all intersections of elements of $ {A^{\ast}}$ partially ordered by $ X \leq Y \Leftrightarrow Y \subseteq X$. Let $ M({\mathcal{A}^{\ast}})$ be $ \mathbb{C}{\mathbb{P}^2} - \cup {\mathcal{A}^{\ast}}$ where $ \cup {\mathcal{A}^{\ast}} = \cup \{ {l_i}:1 \leq i \leq n\} $. The central problem of the theory of arrangement of lines in $ \mathbb{C}{\mathbb{P}^2}$ is the relationship between $ M({\mathcal{A}^{\ast}})$ and $ L({\mathcal{A}^{\ast}}).$


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Additional Information

DOI: https://doi.org/10.1090/S0273-0979-1993-00409-9
Article copyright: © Copyright 1993 American Mathematical Society

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