{"paper":{"title":"Nonabelian Jacobian of Smooth Projective Surfaces - A Survey","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Igor Reider","submitted_at":"2011-03-28T10:38:38Z","abstract_excerpt":"The nonabelian Jacobian $\\JA$ of a smooth projective surface $X$ is inspired by the classical theory of Jacobian of curves. It is built as a natural scheme interpolating between the Hilbert scheme $\\XD$ of subschemes of length $d$ of $X$ and the stack ${\\bf M}_X (2,L,d)$ of torsion free sheaves of rank 2 on $X$ having the determinant $\\OO_X (L)$ and the second Chern class (= number) $d$. It relates to such influential ideas as variations of Hodge structures, period maps, nonabelian Hodge theory, Homological mirror symmetry, perverse sheave, geometric Langlands program.\n  These relations manife"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.5323","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"}