{"paper":{"title":"Hassett-Tschinkel correspondence: Modality and projective hypersurfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.AG","authors_text":"Elena V. Sharoyko, Ivan V. Arzhantsev","submitted_at":"2009-12-08T12:18:21Z","abstract_excerpt":"B. Hassett and Yu. Tschinkel (1999) introduced a remarkable correspondence between generically transitive actions of a commutative unipotent algebraic group G and finite-dimensional local algebras. In this paper we develop Hassett-Tschinkel correspondence and calculate modality of generically transitive G-actions on projective spaces, classify actions of modality one, and characterize generically transitive G-actions on projective hypersurfaces of given degree. In particular, actions on degenerate projective quadrics are studied."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0912.1474","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"}