Landau-Ginzburg/Calabi-Yau correspondence for the complete intersections X_{3,3} and X_{2,2,2,2}

Clader, Emily

doi:10.48550/arxiv.1301.5530

Cited by 9 publications

(24 citation statements)

References 14 publications

(66 reference statements)

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“…It is a straightforward verification that the hybrid GLSM virtual cycles constructed in our paper agree with those constructed in [26,31]. Indeed, the absolute perfect obstruction theory and cosection for Rcpt constructed in this paper agree with the ones in the literature (see [24]).…”

Section: Lemma 44supporting

confidence: 84%

“…In Section 4, we study a few examples explicitly. By the first comparison theorem, the reduced virtual cycle of the compact moduli space of stable log R-maps recovers FJRWtheory and Clader's hybrid model when they are constructed using cosection localized virtual cycles [16,26].…”

Section: The Inputmentioning

confidence: 76%

“…Hybrid models. The hybrid GLSM considered in the literature [26,31,25] fit neatly into our set-up, and they form a generalization of the examples of the previous sections. In this paper though, we restrict ourselves to the case of compact type insertions, and to the ∞-stability in order to include non-GIT quotients.…”

Section: Lemma 44mentioning

confidence: 99%

“…On the algebraic side, an approach using the cosection localization [37] to construct the GLSM virtual cycle was discovered in [15,16] in the narrow case, and in general in [14,38]. Along the cosection approach, some hybrid models were studied in [26], and a general algebraic theory of GLSM for (compact-type sectors of) GIT targets was put on a firm mathematical footing by Fan, Jarvis and the third author [31]. A further algebraic approach for broad sectors using matrix factorizations has been developed in [46,25], while an analytic approach has been developed in [29], [47].…”

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confidence: 99%

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The logarithmic gauged linear sigma model

Chen,

Janda,

Ruan

2019

Preprint

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We introduce the notion of log R-maps, and develop a proper moduli stack of stable log R-maps in the case of a hybrid gauged linear sigma model. Two virtual cycles (canonical and reduced) are constructed for these moduli stacks. The main results are two comparison theorems relating the reduced virtual cycle to the cosection localized virtual cycle, as well as the reduced virtual cycle to the canonical virtual cycle. This sets the foundation for a new technique for computing higher genus Gromov-Witten invariants of compact Calabi-Yau manifolds. Contents 1. Introduction 1 2. Logarithmic R-maps 7 3. A tale of two virtual cycles 16 4. Examples 28 5. Properties of the stack of stable logarithmic R-maps 30 6. Reducing perfect obstruction theories along boundary 42 References 47

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Section: Lemma 44supporting

confidence: 84%

Section: The Inputmentioning

confidence: 76%

Section: Lemma 44mentioning

confidence: 99%

mentioning

confidence: 99%

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The logarithmic gauged linear sigma model

Chen,

Janda,

Ruan

2019

Preprint

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“…The first genus-zero LG/CY correspondence was proved for the quintic threefold by Chiodo and Ruan ([10]). It has since been proven for several other classes of targets, including Calabi-Yau hypersurfaces in weighted projective spaces ( [8]), many classes of Calabi-Yau complete intersections in weighted projective spaces ( [14,15]), and some other examples ( [28,31]). (Acosta ([3]) also developed a similar correspondence for non-Calabi-Yau hypersurfaces in weighted projective spaces.)…”

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confidence: 99%

Gromov-Witten theory of toroidal orbifolds and GIT wall-crossing

Silversmith

2016

Preprint

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Toroidal 3-orbifolds (S 1 ) 6 /G, for G a finite group, were some of the earliest examples of Calabi-Yau 3-orbifolds to be studied in string theory. While much mathematical progress towards the predictions of string theory has been made in the meantime, most of it has dealt with hypersurfaces in toric varieties. As a result, very little is known about curve-counting theories on toroidal orbifolds. In this paper, we initiate a program to study mirror symmetry and the Landau-Ginzburg/Calabi-Yau (LG/CY) correspondence for toroidal orbifolds. We focus on the simplest example [E 3 /µ3], where E ⊆ P 2 is the elliptic curve V(x 3 0 +x 3 1 +x 3 2 ). We study this orbifold from the point of GIT wall-crossing using the gauged linear sigma model, a collection of moduli spaces generalizing spaces of stable maps. Our main result is a mirror symmetry theorem that applies simultaneously to the different GIT chambers. Using this, we analyze wall-crossing behavior to obtain an LG/CY correspondence relating the genus-zero Gromov-Witten invariants of [E 3 /µ3] to generalized Fan-Jarvis-Ruan-Witten invariants.

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Mirror Symmetry Constructions

Clader

Ruan

2018

B-Model Gromov-Witten Theory

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The following notes are based on lectures by Yongbin Ruan during a special semester on the B-model at the University of Michigan in Winter 2014. No claim to originality is made for anything contained within.The authors would like to thank Mark Shoemaker for his detailed and valuable comments. Thanks are also due to Kentaro Hori for answering many of the authors' questions, and to all of the students in the course on which these notes are based, without whom many corrections and clarifications would not have been made. The authors were partially supported by NSF RTG grant 1045119.

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Landau-Ginzburg/Calabi-Yau correspondence for the complete intersections X_{3,3} and X_{2,2,2,2}

Cited by 9 publications

References 14 publications

The logarithmic gauged linear sigma model

The logarithmic gauged linear sigma model

Gromov-Witten theory of toroidal orbifolds and GIT wall-crossing

Mirror Symmetry Constructions

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