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Boogruimten en contactloci van arrangementen van hypervlakken / Arc spaces and contact loci of hyperplane arrangements

  • Tran, Quang Tue; 117932;
Publication Date
Feb 19, 2024
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In this thesis we study the contact loci and restricted contact loci of hyperplane multi-arrangements. We decompose any contact locus of a hyperplane multi-arrangement into connected components, each component is the complement of a hyperplane arrangement. Based on this, we give an explicit expression for their cohomology rings and show that they are combinatorial invariants. We compute the naive motivic zeta function of any hyperplane multi-arrangement and express it as a rational function, without using resolution of singularities. We also give a decomposition into connected components for any restricted contact locus, where each component is the Milnor fiber of an associated hyperplane arrangement. Additionally, we prove the degeneracy of a spectral sequence related to the restricted contact loci of a hyperplane arrangement and which conjecturally computes algebraically the Floer cohomology of iterates of the Milnor monodromy. We also give formulas for the Betti numbers of contact loci and restricted contact loci in generic cases. / status: published

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