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Showing 1 to 2 of 2 for “"Humbert surface"”.
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Explicit moduli spaces for curves of genus 1 and 2
… modules. In particular, we study the moduli surfaces $Z_{N,r}$ which parametrise $N$-congruences of elliptic curves which raise the Weil pairing to a power of $r$. We first study the birational geometry of the surfaces $Z_{N,r}^{\text{sym}}$ which arise as quotients of the surfaces $Z_{N,r}$ …
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Curves of genus 2 and quadratic forms
… C of genus 2. This form, known as the refined Humbert invariant, was introduced by Kani (1994). Our first main result is the classification of those imprimitive ternary quadratic forms which can occur as one of the forms qC, for some curve C of genus 2. We use this classification to classify …