{"paper":{"title":"Rational curves on \\bar{M}_g and K3 surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Luca Benzo","submitted_at":"2012-08-16T08:59:01Z","abstract_excerpt":"Let $(S,L)$ be a smooth primitively polarized K3 surface of genus $g$ and $f:X \\rightarrow \\mathbb{P}^1$ the fibration defined by a linear pencil in $|L|$. For $f$ general and $g \\geq 7$, we work out the splitting type of the locally free sheaf $\\Psi^{*}_f T_{{\\overline{M}}_g}$, where $\\Psi_f$ is the modular morphism associated to $f$. We show that this splitting type encodes the fundamental geometrical information attached to Mukai's projection map $\\mathcal{P}_g \\rightarrow \\overline{\\mathcal{M}}_g$, where $\\mathcal{P}_g$ is the stack parameterizing pairs $(S,C)$ with $(S,L)$ as above and $C"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.3317","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}