{"paper":{"title":"A Fock space approach to Severi degrees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Rahul Pandharipande, Yaim Cooper","submitted_at":"2012-10-30T16:01:37Z","abstract_excerpt":"The classical Severi degree counts the number of algebraic curves of fixed genus and class passing through points in a surface. We express the Severi degrees of CP1 x CP1 as matrix elements of the exponential of a single operator M on Fock space. The formalism puts Severi degrees on a similar footing as the more developed study of Hurwitz numbers of coverings of curves. The pure genus 1 invariants of the product E x CP1 (with E an elliptic curve) are solved via an exact formula for the eigenvalues of M to initial order. The Severi degrees of CP2 are also determined by M via the (-1)^(d-1)/d^2 "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.8062","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"}