{"paper":{"title":"Large Genus Asymptotics for Volumes of Strata of Abelian Differentials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.DS","math.GT"],"primary_cat":"math.AG","authors_text":"Amol Aggarwal","submitted_at":"2018-04-15T21:19:41Z","abstract_excerpt":"In this paper we consider the large genus asymptotics for Masur-Veech volumes of arbitrary strata of Abelian differentials. Through a combinatorial analysis of an algorithm proposed in 2002 by Eskin-Okounkov to exactly evaluate these quantities, we show that the volume $\\nu_1 \\big( \\mathcal{H}_1 (m) \\big)$ of a stratum indexed by a partition $m = (m_1, m_2, \\ldots , m_n)$ is $\\big( 4 + o(1) \\big) \\prod_{i = 1}^n (m_i + 1)^{-1}$ as $2g - 2 = \\sum_{i = 1}^n m_i$ tends to $\\infty$. This confirms a prediction of Eskin-Zorich and generalizes some of the recent results of Chen-Moeller-Zagier and Sau"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.05431","kind":"arxiv","version":3},"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/1804.05431/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"}