The 3-fold vertex via stable pairs

Abstract

The theory of stable pairs in the derived category yields an enumerative geometry of curves in 3-folds. We evaluate the equivariant vertex for stable pairs on toric 3-folds in terms of weighted box counting. In the toric Calabi-Yau case, the result simplifies to a new form of pure box counting. The conjectural equivalence with the DT vertex predicts remarkable identities. The equivariant vertex governs primary insertions in the theory of stable pairs for toric varieties. We consider also the descendent vertex and conjecture the complete rationality of the descendent theory for stable pairs.

Typos fixed. 40 pages, 8 figures

References in corpus (3)

• Curve counting via stable pairs in the derived category
• Gromov-Witten theory of A_n-resolutions
• Donaldson-Thomas theory of A_n x P^1

Cited by in corpus (43)

• Stability structures, motivic Donaldson-Thomas invariants and cluster transformations
• Curve counting via stable pairs in the derived category
• Stable pairs and BPS invariants
• Refined stable pair invariants for E-, M- and [p,q]-strings
• Moduli of ADHM Sheaves and Local Donaldson-Thomas Theory
• $K$-theoretic DT/PT correspondence for toric Calabi-Yau 4-folds
• Curve counting and DT/PT correspondence for Calabi-Yau 4-folds
• Gromov-Witten/Pairs descendent correspondence for toric 3-folds
• Gromov-Witten/Donaldson-Thomas correspondence for toric 3-folds
• The Stringy Instanton Partition Function
• The refined BPS index from stable pair invariants
• Generating functions of stable pair invariants via wall-crossings in derived categories
• Stable pair invariants of local Calabi-Yau 4-folds
• Descendents on local curves: Rationality
• Quantum Cohomology and Quantum Hydrodynamics from Supersymmetric Quiver Gauge Theories
• The virtual K-theory of Quot schemes of surfaces
• Elliptic Blowup Equations for 6d SCFTs. IV: Matters
• Hilbert schemes and stable pairs: GIT and derived category wall crossings
• Cobordism invariants of the moduli space of stable pairs
• Combinatorics of the double-dimer model
• Stable reflexive sheaves and localization
• Quasimaps and stable pairs
• Descendents on local curves: Stationary theory
• Stable pair invariants of surfaces and Seiberg-Witten invariants
• Enumerative invariants and wall-crossing formulae in abelian categories
• Double nested Hilbert schemes and the local stable pairs theory of curves
• Gauge origami and quiver W-algebras III: Donaldson--Thomas $qq$-characters
• Rank 2 wall-crossing and the Serre correspondence
• The combinatorial PT-DT correspondence
• Curve-counting invariants for crepant resolutions
• Relative orbifold Pandharipande-Thomas theory and the degeneration formula
• Gauge origami and quiver W-algebras IV: Pandharipande--Thomas $qq$-characters
• On the fixed locus of framed instanton sheaves on ${\mathbb{P}}^3$
• EGL formula for DT/PT theory of local curves
• Moduli spaces of semistable pairs on projective Deligne-Mumford stacks
• The 4-fold Pandharipande--Thomas vertex and Jeffrey--Kirwan residue
• Weighted Euler characteristic of the moduli space of higher rank Joyce-Song pairs
• Gromov--Witten/Pandharipande--Thomas correspondence via conifold transitions
• Double-dimer condensation and the PT-DT correspondence
• The orbifold DT/PT vertex correspondence
• Rank 2 sheaves on toric 3-folds: classical and virtual counts
• Gromov-Witten invariants of toric Calabi-Yau threefolds
• Hilbert Schemes, Donaldson-Thomas Theory, Vafa-Witten and Seiberg Witten theories