{"paper":{"title":"Notes on diagonals of the product and symmetric variety of a surface","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Luca Scala","submitted_at":"2015-10-16T14:05:31Z","abstract_excerpt":"Let $X$ be a smooth quasi-projective algebraic surface and let $\\Delta_n$ the big diagonal in the product variety $X^n$. We study cohomological properties of the ideal sheaves $\\mathcal{I}^k_{\\Delta_n}$ and their invariants $(\\mathcal{I}^k_{\\Delta_n})^{\\mathfrak{S}_n}$ by the symmetric group, seen as ideal sheaves over the symmetric variety $S^nX$. In particular we obtain resolutions of the sheaves of invariants $(\\mathcal{I}_{\\Delta_n})^{\\mathfrak{S}_n}$ for $n = 3,4$ in terms of invariants of sheaves over $X^n$ whose cohomology is easy to calculate. Moreover, we relate, via the Bridgeland-Ki"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.04889","kind":"arxiv","version":2},"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"}