Stability of syzygy bundles on varieties of Picard number one
Chen Jiang, Peng Ren

TL;DR
This paper establishes a criterion for the slope-stability of syzygy bundles on smooth projective varieties with Picard number one, and demonstrates stability across various classes of such varieties including Fano, Calabi–Yau, and hyperkähler types.
Contribution
It provides a new criterion for slope-stability of syzygy bundles based on Hilbert polynomial and proves stability for numerous classes of varieties with Picard number one.
Findings
Proves stability of syzygy bundles on Fano and Calabi–Yau complete intersections
Establishes stability on hyperkähler and abelian varieties of Picard number 1
Demonstrates stability on rational homogeneous and weak Calabi–Yau varieties of dimension ≤4
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 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, hyperk\"ahler varieties of Picard number 1, abelian varieties of Picard number , rational homogeneous varieties of Picard number 1, weak Calabi--Yau varieties of Picard number of dimension , and Fano varieties of Picard number of dimension . Also we prove the stability of syzygy bundles on all hyperk\"ahler varieties.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Tensor decomposition and applications · Meromorphic and Entire Functions
