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Hyperelliptic odd coverings | | Riccardo Moschetti
; Gian Pietro Pirola
; | | Date: |
24 Nov 2020 | | Abstract: | We investigate a class of odd (ramification) coverings $C o mathbb{P}^1$
where $C$ is hyperelliptic, its Weierstrass points maps to one fixed point of
$mathbb{P}^1$ and the covering map makes the hyperelliptic involution of $C$
commute with an involution of $mathbb{P}^1$. We show that the total number of
hyperelliptic odd coverings of minimal degree $4g$ is ${3g choose g-1} 2^{2g}$
when $C$ is general. Our study is approached from three main perspectives: if a
fixed effective theta characteristic is fixed they are described as a solution
of a certain class of differential equations; then they are studied from the
monodromy viewpoint and a deformation argument that leads to the final
computation. | | Source: | arXiv, 2011.12159 | | Services: | Forum | Review | PDF | Favorites | |
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