Curve counting and DT/PT correspondence for Calabi-Yau 4-folds

DOI10.1016/j.aim.2020.107371zbMath1451.14122arXiv1903.12171OpenAlexW2924752114MaRDI QIDQ2213772

Martijn Kool, Yalong Cao

Publication date: 3 December 2020

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1903.12171

zbMATH Keywords

DT/PT correspondencecurve countingCalabi-Yau 4-folds

Mathematics Subject Classification ID

(4)-folds (14J35) Calabi-Yau manifolds (algebro-geometric aspects) (14J32) Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects) (14N35) Mirror symmetry (algebro-geometric aspects) (14J33)

Related Items

Stable pairs and Gopakumar-Vafa type invariants for Calabi-Yau \(4\)-folds ⋮ Yang–Mills theories on geometric spaces ⋮ Curve counting via stable objects in derived categories of Calabi-Yau 4-folds ⋮ Gopakumar-Vafa type invariants on Calabi-Yau 4-folds via descendent insertions ⋮ Stable pairs and Gopakumar-Vafa type invariants on holomorphic symplectic 4-folds ⋮ Counting sheaves on Calabi-Yau 4-folds. I ⋮ A Donaldson-Thomas crepant resolution conjecture on Calabi-Yau 4-folds ⋮ The 4-fold Pandharipande-Thomas vertex ⋮ Probing M-theory with tetrahedron instantons ⋮ Correspondence of Donaldson-Thomas and Gopakumar-Vafa invariants on local Calabi-Yau 4-folds over \(V_5\) and \(V_{22}\) ⋮ Charging solid partitions ⋮ Counting perverse coherent systems on Calabi-Yau 4-folds ⋮ Tautological stable pair invariants of Calabi-Yau 4-folds ⋮ Canonical vertex formalism in DT theory of toric Calabi-Yau \(4\)-folds ⋮ \(K\)-theoretic DT/PT correspondence for toric Calabi-Yau 4-folds

Cites Work

• Shifted symplectic structures
• The 3-fold vertex via stable pairs
• Curve counting via stable pairs in the derived category
• The moment map and equivariant cohomology
• The intrinsic normal cone
• Genus zero Gopakumar-Vafa type invariants for Calabi-Yau 4-folds
• Zero-dimensional Donaldson-Thomas invariants of Calabi-Yau 4-folds
• Magnificent four with colors
• \(K\)-theoretic DT/PT correspondence for toric Calabi-Yau 4-folds
• Curve counting via stable objects in derived categories of Calabi-Yau 4-folds
• Orientability of moduli spaces of \(\mathrm{Spin}(7)\)-instantons and coherent sheaves on Calabi-Yau 4-folds
• Counting conics on sextic \(4\)-folds
• Orientability for gauge theories on Calabi-Yau manifolds
• Virtual fundamental classes for moduli spaces of sheaves on Calabi-Yau four-folds
• Enumerative geometry of Calabi-Yau 4-folds
• The topological vertex
• Gopakumar-Vafa type invariants on Calabi-Yau 4-folds via descendent insertions
• Curve counting theories via stable objects I. DT/PT correspondence
• Hall algebras and curve-counting invariants
• Reduced classes and curve counting on surfaces I: theory
• Stable Pair Invariants of Local Calabi–Yau 4-folds
• Genus zero Gopakumar–Vafa type invariants for Calabi–Yau 4-folds II: Fano 3-folds
• Relative Donaldson-Thomas theory for Calabi-Yau 4-folds
• Gromov–Witten theory and Donaldson–Thomas theory, I

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