Algebraic Geometry Working Seminar

Robert Harris, Department of Pure Mathematics, University of Waterloo

"Abelian Covers and Line Arrangements in CP^2"

​Branched covers commonly show up in the study of 4-manifolds as they provide access to a large class of complex surfaces while yielding invariants which are relatively easy to compute. For this talk we will focus on branched covers for which the covering map represents a quotient by an Abelian group. We begin by looking at results that provide the existence of such Abelian covers under certain conditions. Then we will see how these results can be used to explicitly construct examples of Abelian covers by considering the union of lines in CP^2. In the remaining time we will look at some of the applications of these constructions in the context of the classification of complex surfaces and the geography problem for simply connected 4-manifolds.

This seminar will be held jointly online and in person:

• Room: MC 5403
• Zoom information: Meeting ID: 817 1030 9714; Passcode: 063438