2024/11/30 by Jiang, Chen, Ren, Peng
#14H60 (Primary) 14C20 #14J32 #14J42 #14J45 #14M10 #14M17 (Secondary) #Algebraic Geometry (math.AG) #FOS: Mathematics
paper · doi:10.48550/arxiv.2412.00476
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 ≤ 4, and Fano varieties of Picard number 1 of dimension ≤5. Also we prove the stability of syzygy bundles on all hyperkähler varieties.