On the Decomposition of the Small Diagonal of a K3 Surface

TL;DR

This paper provides an explicit, projective space-based proof of Beauville and Voisin's theorem on the decomposition of the small diagonal of a K3 surface, offering a different approach from previous methods.

Contribution

It introduces a new explicit proof technique for the decomposition of the small diagonal of a K3 surface, avoiding reliance on elliptic curve families.

Findings

Proof is explicit and geometric

Works with embedding in projective space

Different from previous elliptic curve methods

Abstract

We give a new proof of the theorem of Beauville and Voisin about the decomposition of the small diagonal of a K3 surface S. Our proof is explicit and works with the embedding of S in a projective space. It is different from the one used by Beauville and Voisin, which employed the existence of one-parameters families of elliptic curves.