Some Remarks on H-stability of syzygy bundle on algebraic surface

2020/08/25 by H. Torres-López, Torres-López, H., Alexis G. Zamora +1
Mathematics · #Algebraic Geometry and Number Theory #Geometry and complex manifolds #Advanced Algebra and Geometry

paper · pdf · doi:10.48550/arxiv.2008.11255

Abstract

Let L be a globally generated line bundle over a smooth irreducible complex projective surface X. The syzygy bundle M_L is the kernel of the evaluation map H⁰(L)⊗\mathcal O_X→ L. We prove the L-stability of M_L for Hirzebruch surfaces, del Pezzo surfaces and Enriques surfaces. The (-K_X)-stability of syzygy bundles M_L over del Pezzo surfaces is also obtained.

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