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We prove that a smooth plane quartic admits a unique GIT-stable plane model if and only if its stable reduction is non-hyperelliptic. When this holds, the stable model is obtained from the GIT-stable plane model by a canonical local modification supported at the cusps of the special fiber. This description isolates the geometric mechanism behind the hyperelliptic/non-hyperelliptic dichotomy. The explicit cusp-resolution step is treated separately and is part of the accompanying implementation.
From: Stefan Wewers [view email]
[v1]
Thu, 11 Jun 2026 19:43:52 UTC (355 KB)
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