{"paper":{"title":"Deformations of cones over hyperelliptic curves","license":"","headline":"","cross_cats":["math.AG"],"primary_cat":"alg-geom","authors_text":"Jan Stevens","submitted_at":"1993-03-23T13:24:46Z","abstract_excerpt":"We determine the versal deformation of cones, in the simplest case: cones over hyperelliptic curves of high degree. In particular, we show that for  degree $4g+4$, the highest degree for which interesting deformations exist, the number of smoothing components is $2^{2g+1}$ ($g\\neq3$).\n  We review in a general setting the relation of $T^1(-1)$ with Wahl's Gaussian map. We prove that $T^1(-1)$ vanishes for a general curve and an arbitrary embedding line bundle of degree at least $2g+11$. To find $T^2$ for hyperelliptic cones   with the Main Lemma of [Behnke--Christophersen], we compute  $T^1$ fo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"alg-geom/9303003","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"}