# Chow groups of conic bundles in $\mathbb P^5$ and the Generalised Bloch's conjecture

## TL;DR

This paper investigates the Fano surface of a conic bundle in projective 5-space, providing obstructions to the involution's action on algebraically trivial zero cycles, contributing to the understanding of the generalized Bloch's conjecture.

## Contribution

It introduces an obstruction to the involution acting trivially on zero cycles on the Fano surface of a conic bundle, advancing the study of algebraic cycles and Bloch's conjecture.

## Key findings

- Obstruction to involution acting trivially on zero cycles
- Insights into the structure of algebraic cycles on Fano surfaces
- Contributions to the generalized Bloch's conjecture

## Abstract

Consider the Fano surface of a conic bundle embedded in $\mathbb P^5$. Let $i$ denote the natural involution acting on this surface. In this note we provide an obstruction to the identity action of the involution on the group of algebraically trivial zero cycles modulo rational equivalence on the surface.