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تسجيل مستخدم جديدReduction type of genus-3 curves in a special stratum of their moduli space
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We study a 3-dimensional stratum $mathcal{M}_{3,V}$ of the moduli space $mathcal{M}_3$ of curves of genus $3$ parameterizing curves $Y$ that admit a certain action of $V= C_2times C_2$. We determine the possible types of the stable reduction of these curves to characteristic different from $2$. We define invariants for $mathcal{M}_{3,V}$ 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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