Semistability of Syzygy Bundles Associated to Ulrich Bundles on Projective Varieties of Arbitrary Dimension

2026/06/30 by Soham Mondal
Mathematics · #math.AG

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Abstract

Let X be a smooth irreducible projective variety of dimension n≥ 3 over an algebraically closed field of characteristic zero, polarized by a very ample line bundle \OO_X(1). Let \E be an Ulrich bundle on X. We prove that there exists an explicitly computable integer M≫ 0 such that for every m≥ M the global syzygy bundle S_\E(m) is slope semistable with respect to \OO_X(1). This confirms Conjecture~3.11 of Miró-Roig.

Related

• Koszul property of Ulrich bundles and rationality of moduli spaces of stable bundles on Del Pezzo surfaces
• Semistablity of syzygy bundles on projective spaces in positive characteristics
• Stability of syzygy bundles on smooth projective varieties
• Looking out for stable syzygy bundles
• Stability of Syzygy bundles corresponding to stable vector bundles on algebraic surfaces