Stability of syzygy bundles on varieties of Picard number one

Abstract

We give a criterion for slope-stability of the syzygy bundle of a globally generated ample line bundle on a smooth projective variety of Picard number $1$ in terms of Hilbert polynomial. As applications, we prove the stability of syzygy bundles on many varieties, such as smooth Fano or Calabi--Yau complete intersections, hyperkähler varieties of Picard number 1, abelian varieties of Picard number $1$, rational homogeneous varieties of Picard number 1, weak Calabi--Yau varieties of Picard number $1$ of dimension $\le 4$, and Fano varieties of Picard number $1$ of dimension $\le 5$. Also we prove the stability of syzygy bundles on all hyperkähler varieties.

14 pages, accepted by Int. Math. Res. Not

References in corpus (4)

• Positivity of Riemann-Roch polynomials and Todd classes of hyperkähler manifolds
• Stability of Kernel Sheaves on Del Pezzo Surfaces
• On Stability of Syzygy Bundles
• On the instability of syzygy bundles on toric surfaces