Topological invariance of intersection lattices of arrangements in $\mathbf {CP}^2$
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- by Tan Jiang and Stephen S.-T. Yau PDF
- Bull. Amer. Math. Soc. 29 (1993), 88-93 Request permission
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 $L({\mathcal {A}^{\ast }}).$References
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Additional Information
- © Copyright 1993 American Mathematical Society
- 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