The DT/PT correspondence for smooth curves

Abstract

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 determine, via Quot schemes, the global Donaldson-Thomas theory of a general Abel-Jacobi curve of genus $3$.

arXiv commentMinor changes, published version

References in corpus (7)

• Curve counting via stable pairs in the derived category
• Stable pairs and BPS invariants
• Zero dimensional Donaldson-Thomas invariants of threefolds
• Curve counting on elliptic Calabi-Yau threefolds via derived categories
• Local contributions to Donaldson-Thomas invariants
• Gromov-Witten theory of $K3\times {\mathbb{P}}^1$ and quasi-Jacobi forms
• Curve counting on abelian surfaces and threefolds

Cited by in corpus (5)

• Higher rank K-theoretic Donaldson-Thomas theory of points
• Virtual counts on Quot schemes and the higher rank local DT/PT correspondence
• The local motivic DT/PT correspondence
• The Hilbert scheme of hyperelliptic Jacobians and moduli of Picard sheaves
• Unweighted Donaldson-Thomas theory of the banana 3-fold with section classes