# De Concini-Procesi models of reflection arrangements

### Summary

Describing the geometry and topology of the projective algebraic varieties obtained by blowing up the intersections of the reflecting hyperplanes of a reflection group.

### Supervisor(s)

Associate Professor Anthony Henderson

### Research Location

School of Mathematics and Statistics

### Program Type

PHD

### Synopsis

For any arrangement of hyperplanes in a complex vector space, De Concini and Procesi defined a canonical way to compactify the complement in which the original arrangement is replaced by a normal-crossings divisor. The resulting projective varieties, known as De Concini-Procesi models, are used to study the topology of the arrangement and are also interesting in their own right. For example, in the case of the pure braid arrangement (Coxeter type A) the De Concini-Procesi model is a vitally important object in algebraic geometry: the moduli space of stable genus zero curves with marked points. It is natural to expect that the De Concini-Procesi models of other reflection arrangements have similarly interesting properties.

### Additional Information

A good Honours degree (or equivalent) majoring in some algebraic area of pure mathematics is essential. Prior knowledge of group representation theory and algebraic topology is highly desirable.

The School of Mathematics and Statistics has a large and active Algebra research group including (as of 2008) seven continuing academic and research staff members, three postdoctoral researchers and ten PhD students. The weekly Algebra seminar showcases the research of the group and its many visitors.

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### Keywords

Algebra, geometry, topology, group theory, reflection groups

### Opportunity ID

The opportunity ID for this research opportunity is: **573**

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