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Geometry of the Wiman–Edge monodromy
Journal of Topology and Analysis  (IF0.457),  Pub Date : 2021-09-17, DOI: 10.1142/s1793525321500503
Matthew Stover

The Wiman–Edge pencil is a pencil of genus 6 curves for which the generic member has automorphism group the alternating group A5. There is a unique smooth member, the Wiman sextic, with automorphism group the symmetric group S5. Farb and Looijenga proved that the monodromy of the Wiman–Edge pencil is commensurable with the Hilbert modular group SL2([5]). In this note, we give a complete description of the monodromy by congruence conditions modulo 4 and 5. The congruence condition modulo 4 is new, and this answers a question of Farb–Looijenga. We also show that the smooth resolution of the Baily–Borel compactification of the locally symmetric manifold associated with the monodromy is a projective surface of general type. Lastly, we give new information about the image of the period map for the pencil.