Hodge-to-de Rham degeneration and quasihomogeneous singularities of curves

TL;DR

This paper links the degeneration of Hodge-to-de Rham and Hochschild-to-cyclic spectral sequences at E2 to the condition that all singularities are quasihomogeneous plane curve singularities in integral projective curves.

Contribution

It establishes an equivalence between spectral sequence degeneration and quasihomogeneity of singularities for certain algebraic curves.

Findings

Degeneration at E2 of Hodge-to-de Rham sequence occurs iff singularities are quasihomogeneous plane curves.

Hochschild-to-cyclic spectral sequence degenerates at E2 under the same quasihomogeneity condition.

Provides criteria connecting spectral sequence behavior with singularity types in algebraic geometry.

Abstract

We study the Hodge-to-de Rham spectral sequence for integral projective curves with local complete intersection singularities. We prove that degeneration at the E2-page is equivalent to requiring every singularity to be a quasihomogeneous plane curve singularity. We also show that, in the same local complete intersection setting, the Hochschild-to-cyclic spectral sequence degenerates at the E2-page if and only if the same condition holds