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Investigate the stability of syzygy bundles associated with Ulrich bundles on smooth K3 surfaces and Fano varieties.

April 15, 2026Open Access

Stability of Syzygy Bundles of Ulrich Bundles

Key Points

Investigate the stability of syzygy bundles associated with Ulrich bundles on smooth K3 surfaces and Fano varieties.
Examined smooth K3 surfaces and Fano varieties with specific dimensional properties.
Defined syzygy bundles as kernels of evaluation maps for Ulrich bundles.
Applied mathematical conditions to establish semistability.
Proved that the syzygy bundle defined from an Ulrich bundle is semistable.
Characterized conditions under which the stability holds, specifically for varieties of index greater than or equal to n-2.
Established connections between geometric properties of varieties and the stability of the associated syzygy bundles.

Abstract

Abstract Let X be either a smooth K3 surface or a smooth Fano variety (i. e. , -KX - K X is ample) of dimension n and index iX n-2 i X ≥ n - 2 and let E E be an initialized Ulrich bundle on X. In this paper, we show that the syzygy bundle S ₄ S E, defined as the kernel of the evaluation map eval: H^0 (X, E) Oₗ E, e v a l: H 0 (X, E) ⊗ O X → E, is semistable.

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Authors

Rosa M. Miró-Roig

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Mediterranean Journal of Mathematics

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Stability of Syzygy Bundles of Ulrich Bundles

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Abstract

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