Global Mirrors and Discrepant Transformations for Toric Deligne-Mumford Stacks
We introduce a global Landau-Ginzburg model that is mirror to several toric Deligne-Mumford stacks and describe the change of the Gromov-Witten theories under discrepant transformations. We prove a formal decomposition of the quantum cohomology D-modules (and of the all-genus Gromov-Witten potential...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2020 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2020
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/210718 |
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| Cite this: | Global Mirrors and Discrepant Transformations for Toric Deligne-Mumford Stacks. Hiroshi Iritani. SIGMA 16 (2020), 032, 111 pages |
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Iritani, Hiroshi 2025-12-15T15:32:02Z 2020 Global Mirrors and Discrepant Transformations for Toric Deligne-Mumford Stacks. Hiroshi Iritani. SIGMA 16 (2020), 032, 111 pages 1815-0659 2020 Mathematics Subject Classification: 14N35;14J33;53D45 arXiv:1906.00801 https://nasplib.isofts.kiev.ua/handle/123456789/210718 https://doi.org/10.3842/SIGMA.2020.032 We introduce a global Landau-Ginzburg model that is mirror to several toric Deligne-Mumford stacks and describe the change of the Gromov-Witten theories under discrepant transformations. We prove a formal decomposition of the quantum cohomology D-modules (and of the all-genus Gromov-Witten potentials) under a discrepant toric wall-crossing. In the case of weighted blowups of weak-Fano compact toric stacks along toric centres, we show that an analytic lift of the formal decomposition corresponds, via the Γˆ-integral structure, to an Orlov-type semiorthogonal decomposition of topological K-groups. We state a conjectural functoriality of Gromov-Witten theories under discrepant transformations in terms of a Riemann-Hilbert problem. I would like to thank Pedro Acosta, Arend Bayer, Andrea Brini, Tom Coates, Alessio Corti, Sergey Galkin, Vasily Golyshev, Eduardo Gonz´alez, Claus Hertling, Yuki Hirano, Paul Horja, Yunfeng Jiang, Yuan-Pin Lee, Chiu-Chu Melissa Liu, Wanmin Liu, Thomas Reichelt, Yongbin Ruan, Kyoji Saito, Fumihiko Sanda, Christian Sevenheck, Yota Shamoto, Mark Shoemaker, Takuro Mochizuki, Mauricio Romo, Hsian-Hua Tseng, and Chris Woodward for many insightful discussions and explanations. I also thank the anonymous referees for their careful reading and helpful comments. This work is supported by EPSRC grant EP/E022162/1, and JSPS Kakenhi Grants Number 22740042, 23224002, 24224001, 25400069, 26610008, 16K05127, 16H06335, 16H06337, and 17H06127. Part of this work was done while I was in residence at the Mathematical Sciences Research Institute in Berkeley, California, during the Spring semester of 2018, and the stay was supported by the National Science Foundation under Grant No. DMS-1440140. I thank the organizers and participants of the programme for many stimulating discussions. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Global Mirrors and Discrepant Transformations for Toric Deligne-Mumford Stacks Article published earlier |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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| title |
Global Mirrors and Discrepant Transformations for Toric Deligne-Mumford Stacks |
| spellingShingle |
Global Mirrors and Discrepant Transformations for Toric Deligne-Mumford Stacks Iritani, Hiroshi |
| title_short |
Global Mirrors and Discrepant Transformations for Toric Deligne-Mumford Stacks |
| title_full |
Global Mirrors and Discrepant Transformations for Toric Deligne-Mumford Stacks |
| title_fullStr |
Global Mirrors and Discrepant Transformations for Toric Deligne-Mumford Stacks |
| title_full_unstemmed |
Global Mirrors and Discrepant Transformations for Toric Deligne-Mumford Stacks |
| title_sort |
global mirrors and discrepant transformations for toric deligne-mumford stacks |
| author |
Iritani, Hiroshi |
| author_facet |
Iritani, Hiroshi |
| publishDate |
2020 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| description |
We introduce a global Landau-Ginzburg model that is mirror to several toric Deligne-Mumford stacks and describe the change of the Gromov-Witten theories under discrepant transformations. We prove a formal decomposition of the quantum cohomology D-modules (and of the all-genus Gromov-Witten potentials) under a discrepant toric wall-crossing. In the case of weighted blowups of weak-Fano compact toric stacks along toric centres, we show that an analytic lift of the formal decomposition corresponds, via the Γˆ-integral structure, to an Orlov-type semiorthogonal decomposition of topological K-groups. We state a conjectural functoriality of Gromov-Witten theories under discrepant transformations in terms of a Riemann-Hilbert problem.
|
| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/210718 |
| citation_txt |
Global Mirrors and Discrepant Transformations for Toric Deligne-Mumford Stacks. Hiroshi Iritani. SIGMA 16 (2020), 032, 111 pages |
| work_keys_str_mv |
AT iritanihiroshi globalmirrorsanddiscrepanttransformationsfortoricdelignemumfordstacks |
| first_indexed |
2025-12-17T12:03:41Z |
| last_indexed |
2025-12-17T12:03:41Z |
| _version_ |
1851756926576099328 |