The DT/PT correspondence for smooth curves

  title={The DT/PT correspondence for smooth curves},
  author={Andrea T. Ricolfi},
  journal={Mathematische Zeitschrift},
We show a version of the DT/PT correspondence relating local curve counting invariants, encoding the contribution of a fixed smooth curve in a Calabi–Yau threefold. We exploit a local study of the Hilbert–Chow morphism about the cycle of a smooth curve. We compute, via Quot schemes, the global Donaldson–Thomas theory of a general Abel–Jacobi curve of genus 3. 
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