On the logarithmic Hodge-de Rham spectral sequence for curves on K3 surfaces

TL;DR

This paper demonstrates that for supersingular K3 surfaces, there exists a curve making the logarithmic Hodge-de Rham spectral sequence nondegenerate, revealing new geometric properties of such surfaces.

Contribution

It establishes the existence of a specific curve on supersingular K3 surfaces that affects the degeneracy of the spectral sequence, a novel insight in algebraic geometry.

Findings

Existence of a curve D on supersingular K3 surface X with nondegenerate spectral sequence

Nondegeneracy of the logarithmic Hodge-de Rham spectral sequence for (X,D)

New geometric property of supersingular K3 surfaces related to spectral sequences

Abstract

We show that if $X$ is a supersingular K3 surface then there exists a curve $D$ on $X$ such that the logarithmic Hodge-de Rham spectral sequence for $(X,D)$ is nondegenerate.