Big monodromy for higher Prym representations

Landesman, Aaron¹ ; Litt, Daniel² ; Sawin, Will³

¹Department of Mathematics FAS, Harvard University, Cambridge, MA, United States
²Department of Mathematics, University of Toronto, Toronto, ON, Canada
³Department of Mathematics, Princeton University, Princeton, NJ, United States

Geometry & topology, Tome 29 (2025) no. 5, pp. 2733-2782

Résumé

Let Σg′ →Σg be a cover of an orientable surface of genus g by an orientable surface of genus g′, branched at n points, with Galois group H. Such a cover induces a virtual action of the mapping class group Mod ⁡ g,n+1 of a genus g surface with n + 1 marked points on H1(Σg′, ℂ). When g is large in terms of the group H, we calculate precisely the connected monodromy group of this action. The methods are Hodge-theoretic and rely on a “generic Torelli theorem with coefficients”.

Détail

DOI : 10.2140/gt.2025.29.2733

Keywords: monodromy, Prym representations, curves, mapping class groups, Hodge theory

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