Intersection theory on moduli of smooth complete intersections

TL;DR

This paper develops a general method for calculating the rational Chow rings of moduli spaces of smooth complete intersections, with specific applications to Picard groups, Chow rings, and classical moduli problems.

Contribution

It introduces a unified approach to compute Chow rings of moduli of smooth complete intersections, extending to classical moduli spaces and providing explicit presentations.

Findings

Computed the integral Picard group of the associated stack.

Provided explicit presentations of Chow rings for codimension two cases.

Reproduced and extended results on moduli of curves and K3 surfaces.

Abstract

We provide a general method for computing rational Chow rings of moduli of smooth complete intersections. We specialize this result in different ways: to compute the integral Picard group of the associated stack ; to obtain an explicit presentation of rational Chow rings of moduli of smooth complete intersections of codimension two; to prove old and new results on moduli of smooth curves of genus $\leq 5$ and polarized K3 surfaces of degree $\leq 8$.