Stable quotients and the holomorphic anomaly equation

DOI10.1016/j.aim.2018.05.020zbMath1423.14317arXiv1702.06096OpenAlexW2600119073WikidataQ129754070 ScholiaQ129754070MaRDI QIDQ1639644

Rahul Pandharipande, Hyenho Lho

Publication date: 13 June 2018

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

Full work available at URL: https://arxiv.org/abs/1702.06096

zbMATH Keywords

Gromov-Witten invariantsholomorphic anomaly equationstable quotient

Mathematics Subject Classification ID

Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects) (14N35) Mirror symmetry (algebro-geometric aspects) (14J33)

Related Items (16)

Polynomiality of the equivariant Gromov-Witten theory of $mathbb P^{r-1}$ ⋮ An effective theory of GW and FJRW invariants of quintics Calabi-Yau manifolds ⋮ Stable quotients and the holomorphic anomaly equation ⋮ Virtual cycles on projective completions and quantum Lefschetz formula ⋮ Holomorphic anomaly equations and the Igusa cusp form conjecture ⋮ Holomorphic anomaly equations for the formal quintic ⋮ Finite generation and holomorphic anomaly equation for equivariant Gromov-Witten invariants of \(K_{\mathbb{P}^1\times \mathbb{P}^1}\) ⋮ Open Gromov-Witten theory of \(K_{\mathbb {P}^2}\), \(K_{\mathbb {P}^1\times \mathbb {P}^1}\), \(K_{W\mathbb {P}[ 1,1,2}\), \(K_{\mathbb{F}_1}\) and Jacobi forms] ⋮ Logarithmic quasimaps ⋮ Unnamed Item ⋮ Higher genus FJRW theory for Fermat cubic singularity ⋮ Gromov-Witten invariants of local \(\mathbb{P}^2\) and modular forms ⋮ Quasi-modularity and holomorphic anomaly equation for the twisted Gromov-Witten theory: \(\mathcal{O}(3)\) over \(\mathbb{P}^2\) ⋮ Quasimap wall-crossing for GIT quotients ⋮ Holomorphic anomaly equation for and the Nekrasov-Shatashvili limit of local ⋮ Curves on K3 surfaces in divisibility 2

Cites Work

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• The moduli space of stable quotients
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• Holomorphic anomalies in topological field theories
• Remodeling the B-model
• New calculations in Gromov-Witten theory
• Localization of virtual classes
• The intrinsic normal cone
• Stable quotients and the holomorphic anomaly equation
• Mirror theorem for elliptic quasimap invariants
• Gromov-Witten theory of elliptic fibrations: Jacobi forms and holomorphic anomaly equations
• Quasimap wall-crossings and mirror symmetry
• Higher genus quasimap wall-crossing for semipositive targets
• Holomorphic anomaly equations for the formal quintic
• The topological vertex
• Wall-crossing in genus zero quasimap theory and mirror maps
• Some Properties of Hypergeometric Series Associated with Mirror Symmetry
• Notes on stable maps and quantum cohomology
• Big I-functions

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