Two Criteria For Quasihomogeneity

2024/01/08 by Maitra, Sarasij, Mukundan, Vivek · 1 citation
#13A15 (Primary) #13H05 (Secondary) #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.2401.04254

Abstract

Let (R,\mathfrakm_R,k) be a one-dimensional complete local reduced k-algebra over a field of characteristic zero. The ring R is said to be quasihomogeneous if there exists a surjection Ω_R\twoheadrightarrow \mathfrakm where Ω_R denotes the module of differentials. We present two characterizations of quasihomogeneity of R in the situation when R is a domain: the first one on the valuation semigroup of R and the other on the trace ideal of the module Ω_R.

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