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arXiv · 2606.28861

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

Soham Mondal
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Abstract

Let $X$ be a smooth irreducible projective variety of dimension $n\ge 3$ 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 $M\gg 0$ such that for every $m\ge M$ the global syzygy bundle $S_{\E(m)}$ is slope semistable with respect to $\OO_X(1)$. This confirms Conjecture~3.11 of Mir\'o-Roig.

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Soham Mondal. 2026-06-27. Semistability of Syzygy Bundles Associated to Ulrich Bundles on Projective Varieties of Arbitrary Dimension. https://arxiv.org/abs/2606.28861

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