Gromov-Witten/pairs correspondence for the quintic 3-fold
By R. Pandharipande, Aaron Pixton. 2012
98 citations recorded by the source corpus.
We use the Gromov-Witten/Pairs descendent correspondence for toric 3-folds and degeneration arguments to establish the GW/P correspondence for several compact Calabi-Yau 3-folds (including all CY complete intersections in products of projective spaces). A crucial aspect of the proof is the study of the GW/P correspondence for descendents in relative geometries. Projective bundles over surfaces relative to a section play a special role. The GW/P correspondence for Calabi-Yau complete intersections provides a structure result for the Gromov-Witten invariants in a fixed curve class. After change of variables, the Gromov-Witten series is a rational function in the variable −q = eiu invariant under q ↔ q−1.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/5de3e39140ec886cde925f214a9cba304fa94d87
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In Geometry and Topology
- R. Pandharipande
- Jun Li
- Y. Kiem
- Eleny-Nicoleta Ionel
- Thomas H. Parker
- A. Okounkov
- Georg Oberdieck
- Davesh Maulik
In Mathematical Physics
- R. Pandharipande
- Jun Li
- Y. Kiem
- Eleny-Nicoleta Ionel
- Thomas H. Parker
- Georg Oberdieck
- A. Okounkov
- Davesh Maulik
Citations in the corpus
- Curve Counting on K3 × E, The Igusa Cusp Form χ10, and Descendent Integration (2016, background): “s (32) of the degeneration. The above argument is valid also for the degeneration (33) X= S×E R×E ∪R×E. Since the GW/Pairs correspondence for the relative geometry R×E/F×E follows from the results of [31, 32], we obtain the reduced correspondence for S×E. 5. The full matrix 5.1. The Fock space. The ”
- The Gopakumar-Vafa formula for symplectic manifolds (2013, background): “em. For toric 3-folds, Maulik, Oblomkov, Okounkov and Pandharipande proved the GW/DT correspondence by calculating both sides explicitly a computational tour de force [MOOP]. Pandharipande and Pixton [PP] established the GW/PT correspondence for CY complete intersections in products of projective sp”
- Categorification of Donaldson-Thomas invariants via Perverse Sheaves (2012, methodology): “. Ofcourse, (1)-(3) areconsequencesof(4). Furthermore, establishing the identity (8.1) will equate Definition 8.3 with that introduced by Pandharipande-Thomas [29] for a large class of CY 3-folds (cf. [28]). 8.3. K3-fibered CY 3-folds. In this last subsection, we show that Conjecture 8.5 holds for a p”