{"paper":{"title":"Teichm\\\"uller Discs with Completely Degenerate Kontsevich-Zorich Spectrum","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.DS","authors_text":"David Aulicino","submitted_at":"2012-05-10T19:31:40Z","abstract_excerpt":"We reduce a question of Eskin-Kontsevich-Zorich and Forni-Matheus-Zorich, which asks for a classification of all $\\text{SL}_2(\\mathbb{R})$-invariant ergodic probability measures with completely degenerate Kontsevich-Zorich spectrum, to a conjecture of M\\\"oller's. Let $\\mathcal{D}_g (1)$ be the subset of the moduli space of Abelian differentials $\\mathcal{M}_g$ whose elements have period matrix derivative of rank one. There is an $\\text{SL}_2(\\mathbb{R})$-invariant ergodic probability measure $\\nu$ with completely degenerate Kontsevich-Zorich spectrum, i.e. $\\lambda_1 = 1 > \\lambda_2 = \\cdots ="},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.2359","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"}