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arXiv · 2401.04254

Two Criteria For Quasihomogeneity

Sarasij Maitra·Vivek Mukundan
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Abstract

Let $(R,\mathfrak{m}_R,k)$ 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 $\Omega_R\twoheadrightarrow \mathfrak{m}$ where $\Omega_R$ 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 $\Omega_R$.

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Sarasij Maitra, Vivek Mukundan. 2024-01-08. Two Criteria For Quasihomogeneity. https://arxiv.org/abs/2401.04254

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