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Determinants, Even Instantons and Bridgeland Stability

  • Victor do Valle Pretti

摘要

We provide a systematic way of calculating the quiver region associated with a given exceptional collection. As an application, we prove that \(\mu \) μ -stable sheaves, obtained as the cokernel of morphisms of exceptional \(\mu \) μ -stable bundles, are Bridgeland stable, using the determinant. In the subsequent sections, we focus on the case of even rank 2 instantons over \(\mathbb {P}^3\) P 3 and \(Q_3\) Q 3 , where we prove that instanton sheaves, instanton bundles and perverse instantons are Bridgeland stable and offer a description of the moduli space near its only actual wall.