K-theory of line bundles and smooth varieties

Abstract

We give a $K$-theoretic criterion for a quasi-projective variety to be smooth. If $\mathbb{L}$ is a line bundle corresponding to an ample invertible sheaf on $X$, it suffices that $K_q(X)=K_q(\mathbb{L})$ for all $q\le \dim (X)+1$.

arXiv comment11 pages