Mixed-$\textrm{Spin-P}$ fields of Fermat polynomials

Chang, Huai-Liang; Li, Jun; Li, Weiping; Liu, Melissa Chiu-Chu

doi:10.4310/cjm.2019.v7.n3.a3

Cited by 16 publications

(43 citation statements)

References 10 publications

(6 reference statements)

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“…However one may encounter the following case. Say K P 4 is the total space of the canonical line bundle O P 4 (−5) of P 4 and let W : K P 4 → C be defined by the pairing O P 4 (−5) ⊗ O P 4 (5) → O P 4 with the quintic section 5 i=1 x 5 i of O P 4 (5). Usually the expression W = p 5 i=1 x 5 i is used where p stands for the local coordinate on K P 4 in the noncompact direction.…”

Section: Introductionmentioning

confidence: 99%

“…expected to be responsible for the "genus zero B-twisted correlator of the Landau-Ginzburg space (K P 4 , W )", is not defined to the best of authors' knowledge 2 . On the contrary, in A side, a sequence of works [2,3,4,5,6,7,8,11,12,13,16] study mathematically all genus constructions and properties of LG spaces including (K P 4 , W ) and ([C 5 /Z 5 ], w).…”

Section: Introductionmentioning

confidence: 99%

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Virtual Residue and an Integral Formalism

Chang

2018

J Geom Anal

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We generalize Grothendieck's residues Res ψ s to virtual cases, namely cases when the zero loci of the section s has dimension larger than the expected dimension(zero). We also provide an exponential type integral formalism for the virtual residue, which can be viewed as an analogue of the Mathai-Quillen formalism for localized Euler classes. * Partially supported by Hong Kong GRF grant 16301515 and 16301717. 1 A Landau Ginzburg space is a pair (X, W ) of a complex manifold X and a holomorphic function W : X → C with compact critical locus;

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Virtual Residue and an Integral Formalism

Chang

2018

J Geom Anal

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“…We remark that there is a master space approach for the LG/CY correspondence for all genera by Chang, Li, Li and Liu [7]. Chiodo and Ruan in [11] proved the LG/CY correspondence in genus zero.…”

Section: Comparison Of Gw and Fjrw Via Wall Crossingmentioning

confidence: 95%

A new method toward the Landau–Ginzburg/Calabi–Yau correspondence via quasi-maps

Choi

Kiem

2019

Math. Z.

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The Landau-Ginzburg/Calabi-Yau correspondence claims that the Gromov-Witten invariant of the quintic Calabi-Yau 3-fold should be related to the Fan-Jarvis-Ruan-Witten invariant of the associated Landau-Ginzburg model via wall crossings. In this paper, we consider the stack of quasi-maps with a cosection and introduce sequences of stability conditions which enable us to interpolate between the moduli stack for Gromov-Witten invariants and the moduli stack for Fan-Jarvis-Ruan-Witten invariants.

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“…Thus the claim follows immediately. We replace ξ by ξ ′ , and repeat this procedure finitely many times until (8) does not happen. This gives us a chain of exceptional divisors E 1 , · · · , E k .…”

Section: The Moduli Of Stable Curves With Mixed Weighted Markingsmentioning

confidence: 99%

Higher-genus wall-crossing in Landau–Ginzburg theory

Zhou¹

2020

Advances in Mathematics

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For a Fermat quasi-homogeneous polynomial, we study the associated weighted Fan-Jarvis-Ruan-Witten theory with narrow insertions. We prove a wall-crossing formula in all genera via localization on a master space, which is constructed by introducing an additional tangent vector to the moduli problem. This is a Landau-Ginzburg theory analogue of the higher-genus quasi-map wall-crossing formula proved by Ciocan-Fontanine and Kim. It generalizes the genus-0 result by Ross-Ruan and the genus-1 result by Guo-Ross.It is easy to see that the isomorphism is compatible with the cosections.Then we consider the τ * T M term of the distinguished triangle (15). By Lemma 13, the fixed part is τ * T F 1/r J . Moreover, since pr 1 isétale, we have T F 1/r J ∼ = pr * 1 T M 1/r g,γ J . This finishes the proof that pr * 1 ([M 1/r,ϕ g,γJ ] vir loc ) = [F ϕ J ] vir loc .2 The C * -action on L is only well-defined up to µ µ µr. Nevertheless we can compose the action with the r-th power map C * → C * so that it is well-defined. 1/r 0,γ . However, we can pushforward everything to a point instead. For any non-negative integer c this gives (28) J ψ c φ a , µ + J (−ψ)|(φ bj ) j ∈J 0 0,2|(n−|J|) = µ B (z) z −c−1 ,

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Mixed-$\textrm{Spin-P}$ fields of Fermat polynomials

Cited by 16 publications

References 10 publications

Virtual Residue and an Integral Formalism

Virtual Residue and an Integral Formalism

A new method toward the Landau–Ginzburg/Calabi–Yau correspondence via quasi-maps

Higher-genus wall-crossing in Landau–Ginzburg theory

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