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2018/1/15(Mon)

13:00--14:30 E404

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Moduli geometry of the family of Riemann surfaces associated with the tetrahedron

Thickening the edges of the tetrahedron yields a Riemann surface of genus 3 with a holomorphic action of the tetrahedral group. M. Oka asked what is the defining equation of this Riemann surface as an algebraic curve. In this talk, I will describe the solution of M. Okas question. Unexpectedly the solution forms a 1-parameter family with a sporadic hyperelliptic curve. The image under the moduli map into the moduli space of genus 3 curves is determined. It is a curve passing through the Fermat point and self-intersecting at the Klein point. The universal family around the Fermat point is also described.