Perverse Sheaves and Hyperplane Arrangements

Doctoral Dissertation

Abstract

The category of Perverse Sheaves is known to be an Abelian and Artinian category. As a result, we can talk about the length and decomposition factors of a perverse sheaf. In this thesis we look at a class of perverse sheaves arising from local systems on a complement of a hyperplane arrangement and give a concrete (combinatorial) formula to identify the simple ones; that is, those of length one. By the Riemann-Hilbert correspondence, there is an equivalence of categories between perverse sheaves and regular holonomic D-modules. Therefore, we also obtain the analogous criterion for a class of regular holonomic D-modules on the complement of a hyperplane arrangement.

The above result is obtained by studying the cohomology jump loci on the complement of a hyperplane arrangement and relating it with the support of Sabbah’s specialization complex, which generalizes the nearby cycles complex of Deligne.

Attributes

Attribute NameValues
Author Luis Ernesto Saumell
Contributor Samuel R. Evens, Research Director
Contributor Nero Budur, Research Director
Degree Level Doctoral Dissertation
Degree Discipline Mathematics
Degree Name PhD
Defense Date
  • 2017-05-16

Submission Date 2017-07-11
Subject
  • Mathematics, Algebraic Geometry, Topology, Local systems, Hyperplane Arrangements

Language
  • English

Record Visibility and Access Public
Content License
  • All rights reserved

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