Singularities of elliptic curves in $$K3$$ K 3 surfaces and the Beauville–Voisin zero-cycle

Abstract

Under some hypotheses on the singular type of the one-parameter family of elliptic curves in a primitively polarized $$K3$$ surface $$S$$ determined by its polarization (which is expected to be true for a very general polarized $$K3$$ surface), we give a more geometric proof of the fact that the second Chern class of $$S$$ is equal to $$24 \cdot o_S$$ in the Chow group of $$0$$ -cycles where $$o_S$$ is the Beauville–Voisin canonical $$0$$ -cycle.