On Gromov-Witten theory of projective bundles

Fan, Honglu; Lee, Yuan-Pin

doi:10.48550/arxiv.1607.00740

Cited by 4 publications

(6 citation statements)

References 13 publications

(23 reference statements)

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“…We prove Theorem 1.1 via virtual localization for relative Gromov-Witten invariants [GV05], the topological view for Gromov-Witten theory of Maulik-Pandharipande [MP06], and the results of Fan-Lee [FL16] and Fan [Fan17] on the uniqueness of absolute Gromov-Witten theory of projective bundles.…”

Section: Statement Of the Main Resultsmentioning

confidence: 88%

“…Fan [Fan17] proved this conjecture by first reducing relative Gromov-Witten invariants of ( (N ⊕ Z ), (N )) to absolute Gromov-Witten invariants of (N ⊕ Z ) and (N ) via the absolute/relative correspondence result of Maulik-Pandharipande [MP06] and Hu-Li-Ruan [HLR08], then applying results on the uniqueness of absolute Gromov-Witten invariants of projective bundles proved in [FL16,Fan17].…”

Section: Gromov-witten Theory Of Blow-up Along Complete Intersectionmentioning

confidence: 99%

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Relative Gromov-Witten invariants of projective completions of vector bundles

2018

Sci. China Math.

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It was proved by Fan-Lee and Fan that the absolute Gromov-Witten invariants of two projective bundles (V i ) → X are identified canonically when the total Chern classes c(V 1 ) = c(V 2 ) for two bundles V 1 and V 2 over a smooth projective variety X . In this note we show that for the two projective completions (V i ⊕ ) of V i and their infinity divisors (V i ), the relative Gromov-Witten invariants of ( (V i ⊕ ), (V i )) are identified canonically when c(V 1 ) = c(V 2 ). STATEMENT OF THE MAIN RESULTLet V i → X , i = 1, 2 be two rank n vector bundles over a smooth projective variety X . Denote the total Chern classes of V i , i = 1, 2 bySuppose that c(V 1 ) = c(V 2 ). Let Y i := (V i ⊕ X ) be the projective completion (or projectification) of V i . Denote the projection maps by π i : Y i → X . By Leray-Hirsch we get

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Section: Statement Of the Main Resultsmentioning

confidence: 88%

Section: Gromov-witten Theory Of Blow-up Along Complete Intersectionmentioning

confidence: 99%

Relative Gromov-Witten invariants of projective completions of vector bundles

2018

Sci. China Math.

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“…If the numerical class of f * ([C]) had nontrivial coefficient on ℓ ′ , the assignment of the graph would have involved a balancing condition on the nodes. See [FL16], or [MM15] for details. This general case is not needed in this paper.…”

Section: Edgesmentioning

confidence: 99%

Towards a quantum Lefschetz hyperplane theorem in all genera

Fan¹,

Lee²

2019

Geom. Topol.

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“…In each case we will index fixed locus by suitable bipartite graphs. For the assignment of decorated graphs to invariant stable maps, one can refer to for example [Liu13,FL16], among others. Given Γ a decorated graph for an invariant stable map (C, x 1 , .…”

Section: Theorem 01 and Other Consequencesmentioning

confidence: 99%

“…The explicit localization formula for an arbitrary C * -action is already studied in different papers, for example, [MM15] and [FL16], among others. We have .…”

Section: B2 a Vertex With Edgesmentioning

confidence: 99%

A quantum splitting principle and an application

Fan¹

2019

Annales De l'Institut Fourier

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We propose an analogy of splitting principle in genus-0 Gromov-Witten theory. More precisely, we show how the Gromov-Witten theory of a variety X can be embedded into the theory of the projectivization of a vector bundle over X. An application is also given. Un principe de décomposition quantique et une applicationRésumé. Nous proposons un analogue du principe de décomposition en théorie de Gromov-Witten de genre zéro. Plus précisément, nous montrons comment réaliser la théorie de Gromov-Witten d'une variété X dans la théorie de la projectivisation d'un fibré vectoriel sur X. Nous donnonségalement une application.

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On Gromov-Witten theory of projective bundles

Cited by 4 publications

References 13 publications

Relative Gromov-Witten invariants of projective completions of vector bundles

Relative Gromov-Witten invariants of projective completions of vector bundles

Towards a quantum Lefschetz hyperplane theorem in all genera

A quantum splitting principle and an application

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