Stability of syzygy bundles of Ulrich bundles

Abstract

Let X be either a smooth K3 surface or a smooth Fano variety (i.e. $-K_X$ is ample) of dimension $n$ and index $i_X> n-3$ and let E be an initialized Ulrich bundle on X. In this paper, we show that the syzygy bundle $S(E)$, defined as the kernel of the evaluation map $H^0(X,E)\otimes O_{X}\rightarrow E$, is semistable.