A canonical basis of two-cycles on a K3 surface

TL;DR

This paper constructs a canonical basis of two-cycles on a K3 surface, providing a standard form for their intersection pairing using smooth submanifolds, aiding in the understanding of K3 surface topology.

Contribution

It introduces a canonical basis of two-cycles on K3 surfaces with a standard intersection form, realized via smooth submanifolds, advancing the topological understanding of K3 surfaces.

Findings

Canonical basis with intersection form 2E_8(-1) ⊕ 3H

Realization of basis elements by smooth submanifolds

Standard form for two-cycle intersection pairing

Abstract

We construct a canonical basis of two-cycles, on a $K3$ surface, in which the intersection form takes the canonical form $2E_8(-1) \oplus 3H$. The basic elements are realized by formal sums of smooth submanifolds.