Torsion and cotorsion in the sheaf of Kähler differentials on some mild singularities

2010/12/31 by Daniel Greb, Sönke Rollenske · 9 citations
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Ample line bundle #Geometry and complex manifolds #Gravitational singularity #Projective variety #Sheaf #Torsion (gastropod) #Variety (cybernetics) #math.AC #math.AG #msc:13N10 #msc:14B05 #msc:14F10

paper · pdf · doi:10.4310/mrl.2011.v18.n6.a14

published in Mathematical Research Letters 18(6), 1259-1269 (International Press of Boston) · 12 pages;v2: references updated, Prop. 8 slightly improved

openalex publication_date 2011/01/01 · arxiv created 2011/01/14 · arxiv updated 2015/04/17 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

We give a criterion for the sheaf of Khler differentials on a cone over a smooth projective variety to be torsionfree.Applying this to Veronese embeddings of projective space and using known results about differentials on quotient singularities we show that even for mild, e.g., Gorenstein terminal, singularities the sheaf of Khler differentials will in general have torsion and cotorsion.

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