Cycles that are incidence equivalent to zero

TL;DR

This paper investigates incidence divisors and their relation to Griffiths' conjecture, providing a proof for certain cases using Archimedean height pairing, though some proofs are acknowledged as incorrect.

Contribution

It offers a proof of Griffiths' conjecture on incidence equivalence for specific smooth projective varieties using Archimedean height pairing.

Findings

Confirmed Griffiths' conjecture for varieties with non-vanishing first cohomology

Applied incidence divisors via Archimedean height pairing in the proof

Identified limitations in the proof of Theorem 5.1

Abstract

In this paper, we apply incidence divisors constructed through Archimedean height paring to prove that Griffiths' conjecture on incidence equivalence is correct for a smooth projective variety with first non-vanishing cohomology. (Incidence divisor is insignificant. Theorem 5.1 is significant, but the proof of it presented here is incorrect.)