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3rd NAGC Day 1 Yongqiang Liu: L^2-type invariants and cohomology jump loci for..
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Date: 2022/07/18 Speaker: Yongqiang Liu (USTC) Title: L^2-type invariants and cohomology jump loci for smooth complex quasi- projective varieties Abstract: Let X be a smooth complex quasi-projective variety with a fixed epimorphism ν: π1(X)→Z. We consider the asymptotic behavior of invariants such as Betti numbers and the order of the torsion subgroup of singular homology associated to ν, known as the L^2-type invariants. For degree 1, we give concrete formulas to compute these invariants by geometric information of X. The proof relies on the theory of cohomology jump loci. As an application, when X is a hyperplane arrangement complement, a combinatorial upper bound is given for the number of parallel positive dimension components in degree 1 cohomology jump loci with complex coefficients. Joint work with Fengling Li.
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