Syzygies of some rational homogeneous varieties

TL;DR

This paper investigates the syzygies of rational homogeneous varieties, extending known results about line bundle properties to a broader class of these varieties across different types.

Contribution

It generalizes Manivel's result on Property (N_p) for line bundles on flag varieties to many rational homogeneous varieties of types B, C, D, and G2.

Findings

Extended Property (N_p) results to new classes of rational homogeneous varieties.

Confirmed that p-th powers of ample line bundles satisfy Property (N_p) in these cases.

Broadened understanding of syzygies in the context of algebraic geometry.

Abstract

In this paper, we study syzygies of rational homogeneous varieties. We extend Manivel's result that a $p$-th power of an ample line bundle on a flag variety satisfies Propery $(N_p)$ to many rational homogeneous varieties of type $B$, $C$, $D$, and $G_2$.