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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 $SL2(ℤ[5])$. 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.