A note on homogeneous rank 2 locally nilpotent derivations on k[X,Y,Z]

2022/06/13 by Ghosh, Parnashree
#13F20 #13N15 #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.2206.05906

Abstract

In this article we show that for every prime number p, any irreducible homogeneous locally nilpotent derivations of rank 2 and degree p-2 are triangularizable. Further, we describe the structure of irreducible non-triangularizable homogeneous locally nilpotent derivations of rank 2 and degree pq-2, where p,q are prime numbers. Consequently, we give explicit descriptions of the generators of the image ideals of certain homogeneous locally nilpotent derivations of rank 2.

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