{"paper":{"title":"Fourier-Mukai transform of vector bundles on surfaces to Hilbert scheme","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"D. S. Nagaraj, Indranil Biswas","submitted_at":"2016-05-20T07:11:11Z","abstract_excerpt":"Let $S$ be an irreducible smooth projective surface defined over an algebraically closed field $k$. For a positive integer $d$, let ${\\rm Hilb}^d(S)$ be the Hilbert scheme parametrizing the zero-dimensional subschemes of $S$ of length $d$. For a vector bundle $E$ on $S$, let ${\\mathcal H}(E)\\, \\longrightarrow\\, {\\rm Hilb}^d(S)$ be its Fourier--Mukai transform constructed using the structure sheaf of the universal subscheme of $S\\times {\\rm Hilb}^d(S)$ as the kernel. We prove that two vector bundles $E$ and $F$ on $S$ are isomorphic if the vector bundles ${\\mathcal H}(E)$ and ${\\mathcal H}(F)$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.06229","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"}