{"paper":{"title":"The Abel map for surface singularities I. Generalities and examples","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Andr\\'as N\\'emethi, J\\'anos Nagy","submitted_at":"2018-09-11T08:29:43Z","abstract_excerpt":"Let $(X,o)$ be a complex normal surface singularity. We fix one of its good resolutions $\\widetilde{X}\\to X$, an effective cycle $Z$ supported on the reduced exceptional curve, and any possible (first Chern) class $l'\\in H^2(\\widetilde{X},\\mathbb{Z})$. With these data we define the variety ${\\rm ECa}^{l'}(Z)$ of those effective Cartier divisors $D$ supported on $Z$ which determine a line bundles $\\mathcal{O}_Z(D)$ with first Chern class $l'$. Furthermore, we consider the affine space ${\\rm Pic}^{l'}(Z)\\subset H^1(\\mathcal{O}_Z^*)$ of isomorphism classes of holomorphic line bundles with Chern c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.03737","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"}