{"paper":{"title":"The Moduli Space of Genus Six Curves and K-stability: VGIT and the Hassett-Keel Program","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Junyan Zhao","submitted_at":"2023-04-26T03:17:18Z","abstract_excerpt":"A general curve $C$ of genus six is canonically embedded into the smooth del Pezzo surface $\\Sigma \\subseteq \\mathbb{P}^1 \\times \\mathbb{P}^2$ of degree $5$ as a divisor in the class $\\mathcal{O}_{\\Sigma}(2,2)$. In this article, we study the variation of geometric invariant theory (VGIT) for such pairs $(\\Sigma,C)$, and relate the VGIT moduli spaces to the K-moduli of pairs $(\\Sigma,C)$ and the Hassett-Keel program for moduli of genus six curves. We prove that the K-moduli spaces ${\\overline{M}}^{K}(c)$ give the final several steps in the Hassett-Keel program for ${\\overline{M}}_6$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2304.13259","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2304.13259/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}