Papers › Reduction type of genus-3 curves in a special stratum of their moduli space
Reduction type of genus-3 curves in a special stratum of their moduli space
Irene Bouw, Nirvana Coppola, Pınar Kılıçer, Sabrina Kunzweiler, Elisa Lorenzo García, Anna Somoza
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We study a 3-dimensional stratum ℳ_(3,V) of the moduli space ℳ₃ of curves of genus $3$ parameterizing curves Y that admit a certain action of V= C₂×C₂. We determine the possible types of the stable reduction of these curves to characteristic different from $2$. We define invariants for ℳ_(3,V) and characterize the occurrence of each of the reduction types in terms of them. We also calculate the j-invariant (resp. the Igusa invariants) of the irreducible components of positive genus of the stable reduction of Y in terms of the invariants.
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