REDUCTION TYPES OF GENUS-3 CURVES IN A SPECIAL STRATUM OF THEIR MODULI SPACE
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Abstract
We study a 3-dimensional stratum M_{3,V} of the moduli space M_3 of curves of genus 3 parameterizing curves Y that admit a certain action of V=C_2 × C_2. 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 Y in terms of the invariants.Keywords
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