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Cohomology of arrangements and moduli spaces
Stockholm University, Faculty of Science, Department of Mathematics.
2016 (English)Doctoral thesis, monograph (Other academic)
Abstract [en]

This thesis mainly concerns the cohomology of the moduli spaces ℳ3[2] and ℳ3,1[2] of genus 3 curves with level 2 structure without respectively with a marked point and some of their natural subspaces. A genus 3 curve which is not hyperelliptic can be realized as a plane quartic and the moduli spaces 𝒬[2] and 𝒬1[2] of plane quartics without respectively with a marked point are given special attention. The spaces considered come with a natural action of the symplectic group Sp(6,𝔽2) and their cohomology groups thus become Sp(6,𝔽2)-representations. All computations are therefore Sp(6,𝔽2)-equivariant. We also study the mixed Hodge structures of these cohomology groups.

The computations for ℳ3[2] are mainly via point counts over finite fields while the computations for ℳ3,1[2] primarily uses a description due to Looijenga in terms of arrangements associated to root systems. This leads us to the computation of the cohomology of complements of toric arrangements associated to root systems. These varieties come with an action of the corresponding Weyl group and the computations are equivariant with respect to this action.

Place, publisher, year, edition, pages
Stockholm: Department of Mathematics, Stockholm University , 2016. , 218 p.
Keyword [en]
Algebraic geometry, moduli spaces, cohomology, toric arrangements, equivariant, point counts, finite fields, mixed Hodge structures
National Category
Research subject
URN: urn:nbn:se:su:diva-132822ISBN: 978-91-7649-489-9OAI: diva2:955342
Public defence
2016-11-18, Wallenbergsalen, hus 3, Kräftriket, Roslagsvägen 101, Stockholm, 13:00 (English)
Available from: 2016-10-26 Created: 2016-08-25 Last updated: 2016-10-14Bibliographically approved

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Bergvall, Olof
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