Witten–Dijkgraaf–Verlinde–Verlinde Equation and its Application to Relative Gromov–Witten Theory

Fan, Honglu; Wu, Longting

doi:10.1093/imrn/rnz353

Cited by 10 publications

(13 citation statements)

References 12 publications

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“…. In work [FW19], this recursion is derived as a very particular case of a general WDVV formalism for genus zero Gromov-Witten invariants relative to a smooth divisor.…”

mentioning

confidence: 99%

On an Example of Quiver Donaldson–Thomas/Relative Gromov–Witten Correspondence

Bousseau

2020

International Mathematics Research Notices

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“…. In work [FW19], this recursion is derived as a very particular case of a general WDVV formalism for genus zero Gromov-Witten invariants relative to a smooth divisor.…”

mentioning

confidence: 99%

On an Example of Quiver Donaldson–Thomas/Relative Gromov–Witten Correspondence

Bousseau

2020

International Mathematics Research Notices

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“…Substituting equations (8)-(10) into equation (7) we have the first fundamental form of soliton surface for the Oriented Associativity equation to the system (2)  …”

Section: First Fundamental Form Of a Surfacementioning

confidence: 99%

“…The equation of associativity relation for genus 0 Gromov-Witten (GW) invariants completely solves the classical problem of enumerating complex rational curves in the complex projective space Pn [1]. For genus-0 GW-theory, the associativity of quantum cohomology, which is equivalent to equation of associativity, led to Kontsevich's solution to the classical problem of counting degree d rational curves passing through 3d − 1 general points in P2 [2]. A system of PDE, called open WDVV, that constrains the bulkdeformed superpotential and associated open GW invariants of a Lagrangian submanifold L ⊂ X with a bounding chain [3].…”

Section: Introductionmentioning

confidence: 99%

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Soliton surface associated with the oriented associativity equation for n=3 case

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Myrzakul

Myrzakulov

2019

Int. j. math. phys.

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This paper describes the soliton surfaces approach to the Oriented Associativity equation for n=3 case. The equation of associativity arose from the 2D topological field theory. We constructed the surface associated with the Oriented Associativity equation for n=3 case equations using Sym-Tafel formula, which gives a connection between the classical geometry of manifolds immersed in R m and the theory of solitons. The so-called Sym-Tafel formula simplifies the explicit reconstruction of the surface from the knowledge of its fundamental forms, unifies various integrable nonlinearities and enables one to apply powerful methods of the soliton theory to geometrical problems. The soliton surfaces approach is very useful in construction of the so-called integrable geometries. Indeed, any class of soliton surfaces is integrable. Geometrical objects associated with soliton surfaces (tangent vectors, normal vectors, foliations by curves etc.) usually can be identified with solutions to some nonlinear models (spins, chiral models, strings, vortices etc.). We consider the geometry of surfaces immersed in Euclidean spaces. The Oriented Associativity equation plays a fundamental role in the theory of integrable systems. Such soliton surfaces for the Oriented Associativity equation for n=3 case are considered, and first and second fundamental forms of soliton surfaces are found for this case. Also, we study an area of surfaces for the Oriented Associativity equation for n=3 case.

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“…For related results, see for example [FW20] and reference therein. There exists a nice application of Salmon's pair of inflectional lines.…”

Section: Introductionmentioning

confidence: 99%

A recursive formula for osculating curves

Muratore

2021

Arkiv För Matematik

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Witten–Dijkgraaf–Verlinde–Verlinde Equation and its Application to Relative Gromov–Witten Theory

Abstract: We derive a recursive formula for certain relative Gromov–Witten invariants with a maximal tangency condition via the Witten–Dijkgraaf–Verlinde–Verlinde equation. For certain relative pairs, we get explicit formulae of invariants using the recursive formula.

Cited by 10 publications

References 12 publications

On an Example of Quiver Donaldson–Thomas/Relative Gromov–Witten Correspondence

On an Example of Quiver Donaldson–Thomas/Relative Gromov–Witten Correspondence

Soliton surface associated with the oriented associativity equation for n=3 case

A recursive formula for osculating curves

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