{"paper":{"title":"Correspondences of a K3 surface with itself via moduli of sheaves. I","license":"","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AG","authors_text":"Viacheslav V. Nikulin","submitted_at":"2006-09-08T11:40:49Z","abstract_excerpt":"Let $X$ be an algebraic K3 surface, $v=(r,H,s)$ a primitive isotropic Mukai vector on $X$ and $M_X(v)$ the moduli of sheaves over $X$ with $v$. Let $N(X)$ be Picard lattice of $X$.\n  In math.AG/0309348 and math.AG/0606289, all divisors in moduli of $(X,H)$ (i. e. pairs $H\\in N(X)$ with $\\rk N(X)=2$) implying $M_X(v)\\cong X$ were described. They give some Mukai's correspondences of $X$ with itself.\n  Applying these results, we show that there exists $v$ and a codimension 2 submoduli in moduli of $(X,H)$ (i. e. a pair $H\\in N(X)$ with $\\rk N(X)=3$) implying $M_X(v)\\cong X$, but this submoduli ca"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0609233","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"}