A Griffiths' Theorem for varieties with isolated singularities

TL;DR

This paper extends Griffiths' theorem to varieties with isolated singularities, showing that homological and algebraic equivalence differ for general hypersurface sections in this broader context.

Contribution

It proves a Griffiths' theorem analogue for varieties with isolated singularities, broadening the understanding of algebraic and homological equivalences.

Findings

Homological and algebraic equivalence do not coincide for general hypersurface sections of varieties with isolated singularities.

The result generalizes Griffiths' theorem from smooth to singular varieties.

Provides new insights into the structure of hypersurfaces in singular algebraic varieties.

Abstract

By the fundamental work of Griffiths one knows that, under suitable assumption, homological and algebraic equivalence do not coincide for a general hypersurface section of a smooth projective variety $Y$. In the present paper we prove the same result in case $Y$ has isolated singularities.