Derivations of negative degree on quasihomogeneous isolated complete intersection singularities

2014/03/15 by Michel Granger, Granger, Michel, Mathias Schulze +1
Mathematics · #13N15 #14M10 (Primary) 14H20 (Secondary) #Advanced Differential Equations and Dynamical Systems #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #math.AC #math.AG #msc:13N15 #msc:14H20 #msc:14M10

paper · pdf · doi:10.48550/arxiv.1403.3844

11 pages

openalex publication_date 2014/03/15 · arxiv created 2014/06/26 · arxiv updated 2014/06/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

J. Wahl conjectured that every quasihomogeneous isolated normal singularity admits a positive grading for which there are no derivations of negative weighted degree. We confirm his conjecture for quasihomogeneous isolated complete intersection singularities of either order at least 3 or embedding dimension at most 5. For each embedding dimension larger than 5 (and each dimension larger than 3), we give a counter-example to Wahl's conjecture.

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