Stability of syzygy bundles on smooth projective varieties
Shijie Shang

TL;DR
This paper proves that syzygy bundles associated with sufficiently ample line bundles on smooth projective varieties are slope stable under any polarization, confirming a conjecture by Ein-Lazarsfeld-Mustopa.
Contribution
It establishes the slope stability of syzygy bundles on smooth projective varieties for ample line bundles, settling a previously conjectured property.
Findings
Syzygy bundles are slope stable with respect to any polarization.
The result applies to sufficiently ample line bundles.
It confirms a conjecture by Ein-Lazarsfeld-Mustopa.
Abstract
We prove that the kernel bundle of the evaluation morphism of global sections, namely the syzygy bundle, of a sufficiently ample line bundle on a smooth projective variety is slope stable with respect to any polarization. This settles a conjecture of Ein-Lazarsfeld-Mustopa.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Algebra and Geometry · Homotopy and Cohomology in Algebraic Topology
