{"paper":{"title":"Rank Two Fourier-Mukai Transforms for K3 Surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Antony Maciocia","submitted_at":"2016-08-16T21:34:38Z","abstract_excerpt":"We study rank two locally-free Fourier-Mukai transforms on K3 surfaces and show that they come in two distinct types according to whether the determinant of a suitable twist of the kernel is positive or not. We show that a necessary and sufficient condition on the existence of Fourier-Mukai transforms of rank 2 between the derived categories of K3 surfaces X and Y with negative twisted determinant is that Y is isomorphic to X and there must exist a line bundle with no cohomology. We use these results to prove that all reflexive K3 surfaces (including the degenerate ones) admit Fourier-Mukai tr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.04786","kind":"arxiv","version":3},"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"}