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Torelli group action on the configuration space of a surface

Eduard Looijenga

Eduard Looijenga

Yau Mathematical Sciences Center, Tsinghua University, Beijing, P. R. China

Mathematisch Instituut, Universiteit Utrecht, Nederland

E-mail Address: e.j.n.looijenga@uu.nl

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https://doi.org/10.1142/S1793525321500370Cited by:4 (Source: Crossref)

Abstract

We show that the Torelli group of a closed surface of genus $\geq 3$ $\geq 3$ acts nontrivially on the rational cohomology of the space of $3$ $3$ -element subsets of that surface. This implies that for a Riemann surface of genus $\geq 3$ $\geq 3$ , the mixed Hodge structure on the space of its positive, reduced divisors of degree $3$ $3$ does in general not split over $ℚ$ .

Keywords:

AMSC: 55R80, 14C30, 15K20

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