Direct Images Of Locally Constant Sheaves on Complements to Plane Line Arrangements

University dissertation from Stockholm : Department of Mathematics

Author: Iara Alvarinho Gonçalves; Stockholms Universitet.; [2015]

Keywords: NATURVETENSKAP; NATURAL SCIENCES; Direct Images; Locally Constant Sheaves; Irreducibility; matematik; Mathematics;

Abstract: On the complement $\mathbb{C^{2}}-\bigcup_{i=1}^{n} L_{i}$ (where each $L_{i}$ is a line passing through the origin) to a plane line arrangement $\bigcup_{i=1}^{n} L_{i} \subset \mathbb{C}^{2}$ , a locally constant sheaf of complex vector spaces is given by a multi-index $\alpha\in\mathbb{C}^{n}$ . Using the description of Mac-Pherson and Vilonen ([11] and [12]) we obtain a criterion for the irreducibility of the direct image $Rj_{'}\mathcal{L}_{\alpha}$ as a perverse sheaf, where $j:X\rightarrow\mathbb{C}^{2}$ is the canonical inclusion.