Stability of syzygy bundles

Abstract

We show that given integers $N$, $d$ and $n$ such that $N\ge 2$, $(N,d,n)\ne (2,2,5)$, and $N+1\le n\le \left(\genfrac{}{}{0ex}{}{d+N}{N}\right)$, there is a family of $n$ monomials in $K[X_0,\dots ,X_N]$ of degree $d$ such that their syzygy bundle is stable. Case $N\ge 3$ was obtained independently by Coandǎ with a different choice of families of monomials [Coa09]. For $(N,d,n)=(2,2,5)$, there are $5$ monomials of degree~$2$ in $K[X_0,X_1,X_2]$ such that their syzygy bundle is semistable.

16 pages, to appear in the Proceedings of the American Mathematical Society

References in corpus (1)

• Stability and Unobstructedness of Syzygy Bundles

Cited by in corpus (1)

• Stability of syzygy bundles on varieties of Picard number one