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.
Derivations of negative degree on quasihomogeneous isolated complete intersection singularities.