The geometry of the Humbert surface of discriminant N^2

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• Sam Frengley (University of Cambridge)
• Tuesday 17 October 2023, 14:30-15:30
• MR13.

If you have a question about this talk, please contact Jef Laga.

Building on work of Hermann, I will give a rough classification of the Enriques—Kodaira type of the (generalised) Humbert surface of discriminant N^2.

I will describe the relation between these surfaces and the ‘Hilbert modular surface of discriminant N^2’ (also known as a ‘Modular diagonal quotient surface’) and will give a moduli interpretation in terms of (unordered) pairs of elliptic curves whose mod N Galois representations become isomorphic over a quadratic extension (in analogy to Fricke quotients of modular curves).

This talk is part of the Number Theory Seminar series.

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