A Characterization of Jacobians by the Existence of Picard Bundles (original) (raw)

Abstract

Based on the Matsusaka-Ran criterion we give a criterion to characterize when a principal polarized abelian variety is a Jacobian by the existence of Picard bundles. Contents Introduction 1 Acknowledgements 2 1. Fourier-Mukai transforms for abelian varieties 2 2. Picard Bundles on Jacobians 4 3. A Characterization of Jacobians via Picard Bundles 8 References 10 1. Fourier-Mukai transforms for abelian varieties

Key takeaways

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  1. Existence of Picard bundles characterizes Jacobians of principal polarized abelian varieties (p.p.a.v.s).
  2. Theorem: A p.p.a.v. (A, Θ) is a Jacobian if a WIT g sheaf F exists with specific Chern classes.
  3. Matsusaka-Ran criterion is extended using Picard bundles to identify Jacobians explicitly.
  4. Fourier-Mukai transforms facilitate the study of Picard bundles and their properties.
  5. The paper presents a new criterion for determining Jacobians using geometric properties of curves and sheaves.

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References (13)

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