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A
mathematical theory of the gauged linear sigma model
Huijun Fan, Tyler J Jarvis and Yongbin Ruan |
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Geometry & Topology 22 (2018) 235–303
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Abstract |
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We construct a mathematical theory of Witten’s Gauged Linear Sigma Model (GLSM). Our theory applies to a wide range of examples, including many cases with nonabelian gauge group. Both the Gromov–Witten theory of a Calabi–Yau complete intersection and the Landau–Ginzburg dual (FJRW theory) of can be expressed as gauged linear sigma models. Furthermore, the Landau–Ginzburg/Calabi–Yau correspondence can be interpreted as a variation of the moment map or a deformation of GIT in the GLSM. This paper focuses primarily on the algebraic theory, while a companion article will treat the analytic theory. |
Keywords
gauged linear sigma model, mirror symmetry, Gromov–Witten,
Calabi–Yau, Landau–Ginzburg
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Mathematical Subject Classification 2010
Primary: 14D23, 14L24, 14N35, 53D45, 81T60
Secondary: 14J32, 14L30, 32G81, 81T40
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References |
Publication
Received: 2 November 2015
Revised: 23 December 2016
Accepted: 30 January 2017
Published: 31 October 2017
Proposed: Jim Bryan
Seconded: Richard Thomas, Simon Donaldson
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Authors |
| Huijun Fan | |
| School of Mathematical Science Beijing (Peking) University Beijing China |
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| Tyler J Jarvis | |
| Department of Mathematics Brigham Young University Provo, UT United States |
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| Yongbin Ruan | |
| Mathematics Department University of Michigan Ann Arbor, MI United States |
Beijing International Center for
Mathematical Science Peking University Beijing China |
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