{"paper":{"title":"Hyperpolygon spaces and moduli spaces of parabolic Higgs bundles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SG"],"primary_cat":"math.AG","authors_text":"Alessia Mandini, Leonor Godinho","submitted_at":"2011-01-17T15:32:49Z","abstract_excerpt":"Given an $n$-tuple of positive real numbers $\\alpha$ we consider the hyperpolygon space $X(\\alpha)$, the hyperk\\\"{a}hler quotient analogue to the K\\\"ahler moduli space of polygons in $\\mathbb{R}^3$. We prove the existence of an isomorphism between hyperpolygon spaces and moduli spaces of stable, rank-$2$, holomorphically trivial parabolic Higgs bundles over $\\mathbb{C} \\mathbb{P}^1$ with fixed determinant and trace-free Higgs field. This isomorphism allows us to prove that hyperpolygon spaces $X(\\alpha)$ undergo an elementary transformation in the sense of Mukai as $\\alpha$ crosses a wall in t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.3241","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":""},"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"}