We investigate a class of odd (ramification) coverings C → ℙ1 where C is hyperelliptic, its Weierstrass points map to one fixed point of ℙ1 and the covering map makes the hyperelliptic involution of C commute with an involution of ℙ1. We compute the number of hyperelliptic odd coverings of minimal degree 4g is 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.
Hyperelliptic odd coverings
Moschetti, Riccardo;Pirola, Gian Pietro
2022-01-01
Abstract
We investigate a class of odd (ramification) coverings C → ℙ1 where C is hyperelliptic, its Weierstrass points map to one fixed point of ℙ1 and the covering map makes the hyperelliptic involution of C commute with an involution of ℙ1. We compute the number of hyperelliptic odd coverings of minimal degree 4g is 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.File in questo prodotto:
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