Singularities, mirror symmetry, and the gauged linear sigma model: Summer School, Crossing the walls in enumerative geoemetry, May 21 - June 1, 2018, Snowbird, Utah
This volume contains the proceedings of the workshop Crossing the Walls in Enumerative Geometry, held in May 2018 at Snowbird, Utah. It features a collection of both expository and research articles about mirror symmetry, quantized singularity theory (FJRW theory), and the gauged linear sigma model....
Gespeichert in:
| Weitere Verfasser: | , |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
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Providence, Rhode Island
American Mathematical Society
[2021]
|
| Schriftenreihe: | Contemporary mathematics / American Mathematical Society
volume 763 |
| Online-Zugang: | DE-19 DE-355 Volltext |
| Zusammenfassung: | This volume contains the proceedings of the workshop Crossing the Walls in Enumerative Geometry, held in May 2018 at Snowbird, Utah. It features a collection of both expository and research articles about mirror symmetry, quantized singularity theory (FJRW theory), and the gauged linear sigma model.Most of the expository works are based on introductory lecture series given at the workshop and provide an approachable introduction for graduate students to some fundamental topics in mirror symmetry and singularity theory, including quasimaps, localization, the gauged linear sigma model (GLSM), virtual classes, cosection localization, p-fields, and Saito's primitive forms. These articles help readers bridge the gap from the standard graduate curriculum in algebraic geometry to exciting cutting-edge research in the field.The volume also contains several research articles by leading researchers, showcasing new developments in the field Cover -- Title page -- Contents -- Preface -- Quasimaps and some examples of stacks for everybody -- 1. Introduction -- 2. Motivation for the study of quasimaps -- 3. Quotients in algebraic geometry -- 4. Quasimaps -- 5. Stability and moduli spaces of quasimaps -- 6. Virtual cycles via perfect obstruction theories -- 7. Quasimap -functions -- 8. A formula for the -function -- References -- Introduction to the gauged linear sigma model -- 1. Preliminaries on orbifolds and Gromov-Witten theory -- 2. Fan-Jarvis-Ruan-Witten theory -- 3. The Landau-Ginzburg/Calabi-Yau correspondence -- 4. The hybrid model and the GLSM -- 5. Wall-crossing and the proof of the LG/CY correspondence -- References -- Localization and mirror symmetry -- 0. Introduction -- 1. Equivariant cohomology and localization -- 2. Fan-Jarvis-Ruan-Witten theory of the quintic threefold -- 3. Proof of the Fan-Jarvis-Ruan-Witten mirror theorem -- 4. Gromov-Witten theory of the quintic threefold -- 5. Proof of the Gromov-Witten mirror theorem -- Acknowledgments -- References -- A brief introduction to cosection localization and -fields -- 1. Introduction -- 2. Virtual cycles, obstruction theory (local), and normal cones -- 3. Virtual cycles via intrinsic normal cone (global) -- 4. Cosection localization -- 5. -fields and applications -- Acknowledgments -- References -- Virtual classes for hypersurfaces via two-periodic complexes -- Introduction -- 1. The zero locus of a section -- 2. Stable maps to projective space -- 3. Stable maps to a hypersurface -- 4. Technical assumptions and the "two-step procedure" -- 5. Conclusions and further directions -- Acknowledgments -- References -- Localized Chern characters for 2-periodic complexes and virtual cycles -- 1. Introduction -- 2. Localized Chern characters for 2-periodic complexes -- 3. Virtual fundamental classes |
| Beschreibung: | Description based on publisher supplied metadata and other sources |
| Beschreibung: | 1 Online-Ressource (x,203 Seiten) |
| ISBN: | 9781470464196 |
| DOI: | 10.1090/conm/763 |
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| 520 | 3 | |a This volume contains the proceedings of the workshop Crossing the Walls in Enumerative Geometry, held in May 2018 at Snowbird, Utah. It features a collection of both expository and research articles about mirror symmetry, quantized singularity theory (FJRW theory), and the gauged linear sigma model.Most of the expository works are based on introductory lecture series given at the workshop and provide an approachable introduction for graduate students to some fundamental topics in mirror symmetry and singularity theory, including quasimaps, localization, the gauged linear sigma model (GLSM), virtual classes, cosection localization, p-fields, and Saito's primitive forms. These articles help readers bridge the gap from the standard graduate curriculum in algebraic geometry to exciting cutting-edge research in the field.The volume also contains several research articles by leading researchers, showcasing new developments in the field | |
| 520 | 3 | |a Cover -- Title page -- Contents -- Preface -- Quasimaps and some examples of stacks for everybody -- 1. Introduction -- 2. Motivation for the study of quasimaps -- 3. Quotients in algebraic geometry -- 4. Quasimaps -- 5. Stability and moduli spaces of quasimaps -- 6. Virtual cycles via perfect obstruction theories -- 7. Quasimap -functions -- 8. A formula for the -function -- References -- Introduction to the gauged linear sigma model -- 1. Preliminaries on orbifolds and Gromov-Witten theory -- 2. Fan-Jarvis-Ruan-Witten theory -- 3. The Landau-Ginzburg/Calabi-Yau correspondence -- 4. The hybrid model and the GLSM -- 5. Wall-crossing and the proof of the LG/CY correspondence -- References -- Localization and mirror symmetry -- 0. Introduction -- 1. Equivariant cohomology and localization -- 2. Fan-Jarvis-Ruan-Witten theory of the quintic threefold -- 3. Proof of the Fan-Jarvis-Ruan-Witten mirror theorem -- 4. Gromov-Witten theory of the quintic threefold -- 5. Proof of the Gromov-Witten mirror theorem -- Acknowledgments -- References -- A brief introduction to cosection localization and -fields -- 1. Introduction -- 2. Virtual cycles, obstruction theory (local), and normal cones -- 3. Virtual cycles via intrinsic normal cone (global) -- 4. Cosection localization -- 5. -fields and applications -- Acknowledgments -- References -- Virtual classes for hypersurfaces via two-periodic complexes -- Introduction -- 1. The zero locus of a section -- 2. Stable maps to projective space -- 3. Stable maps to a hypersurface -- 4. Technical assumptions and the "two-step procedure" -- 5. Conclusions and further directions -- Acknowledgments -- References -- Localized Chern characters for 2-periodic complexes and virtual cycles -- 1. Introduction -- 2. Localized Chern characters for 2-periodic complexes -- 3. Virtual fundamental classes | |
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| spelling | Jarvis, Tyler Jamison 1966- (DE-588)173866883 edt Singularities, mirror symmetry, and the gauged linear sigma model Summer School, Crossing the walls in enumerative geoemetry, May 21 - June 1, 2018, Snowbird, Utah Tyler J. Jarvis, Nathan Priddis, editors Providence, Rhode Island American Mathematical Society [2021] © 2021 1 Online-Ressource (x,203 Seiten) txt rdacontent c rdamedia cr rdacarrier Contemporary mathematics / American Mathematical Society volume 763 Description based on publisher supplied metadata and other sources This volume contains the proceedings of the workshop Crossing the Walls in Enumerative Geometry, held in May 2018 at Snowbird, Utah. It features a collection of both expository and research articles about mirror symmetry, quantized singularity theory (FJRW theory), and the gauged linear sigma model.Most of the expository works are based on introductory lecture series given at the workshop and provide an approachable introduction for graduate students to some fundamental topics in mirror symmetry and singularity theory, including quasimaps, localization, the gauged linear sigma model (GLSM), virtual classes, cosection localization, p-fields, and Saito's primitive forms. These articles help readers bridge the gap from the standard graduate curriculum in algebraic geometry to exciting cutting-edge research in the field.The volume also contains several research articles by leading researchers, showcasing new developments in the field Cover -- Title page -- Contents -- Preface -- Quasimaps and some examples of stacks for everybody -- 1. Introduction -- 2. Motivation for the study of quasimaps -- 3. Quotients in algebraic geometry -- 4. Quasimaps -- 5. Stability and moduli spaces of quasimaps -- 6. Virtual cycles via perfect obstruction theories -- 7. Quasimap -functions -- 8. A formula for the -function -- References -- Introduction to the gauged linear sigma model -- 1. Preliminaries on orbifolds and Gromov-Witten theory -- 2. Fan-Jarvis-Ruan-Witten theory -- 3. The Landau-Ginzburg/Calabi-Yau correspondence -- 4. The hybrid model and the GLSM -- 5. Wall-crossing and the proof of the LG/CY correspondence -- References -- Localization and mirror symmetry -- 0. Introduction -- 1. Equivariant cohomology and localization -- 2. Fan-Jarvis-Ruan-Witten theory of the quintic threefold -- 3. Proof of the Fan-Jarvis-Ruan-Witten mirror theorem -- 4. Gromov-Witten theory of the quintic threefold -- 5. Proof of the Gromov-Witten mirror theorem -- Acknowledgments -- References -- A brief introduction to cosection localization and -fields -- 1. Introduction -- 2. Virtual cycles, obstruction theory (local), and normal cones -- 3. Virtual cycles via intrinsic normal cone (global) -- 4. Cosection localization -- 5. -fields and applications -- Acknowledgments -- References -- Virtual classes for hypersurfaces via two-periodic complexes -- Introduction -- 1. The zero locus of a section -- 2. Stable maps to projective space -- 3. Stable maps to a hypersurface -- 4. Technical assumptions and the "two-step procedure" -- 5. Conclusions and further directions -- Acknowledgments -- References -- Localized Chern characters for 2-periodic complexes and virtual cycles -- 1. Introduction -- 2. Localized Chern characters for 2-periodic complexes -- 3. Virtual fundamental classes Priddis, Nathan C. 1983- (DE-588)1233830953 edt Erscheint auch als Druck-Ausgabe 978-1-4704-5700-6 (DE-604)BV047275300 https://doi.org/10.1090/conm/763 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Singularities, mirror symmetry, and the gauged linear sigma model Summer School, Crossing the walls in enumerative geoemetry, May 21 - June 1, 2018, Snowbird, Utah |
| title | Singularities, mirror symmetry, and the gauged linear sigma model Summer School, Crossing the walls in enumerative geoemetry, May 21 - June 1, 2018, Snowbird, Utah |
| title_auth | Singularities, mirror symmetry, and the gauged linear sigma model Summer School, Crossing the walls in enumerative geoemetry, May 21 - June 1, 2018, Snowbird, Utah |
| title_exact_search | Singularities, mirror symmetry, and the gauged linear sigma model Summer School, Crossing the walls in enumerative geoemetry, May 21 - June 1, 2018, Snowbird, Utah |
| title_exact_search_txtP | Singularities, mirror symmetry, and the gauged linear sigma model Summer School, Crossing the walls in enumerative geoemetry, May 21 - June 1, 2018, Snowbird, Utah |
| title_full | Singularities, mirror symmetry, and the gauged linear sigma model Summer School, Crossing the walls in enumerative geoemetry, May 21 - June 1, 2018, Snowbird, Utah Tyler J. Jarvis, Nathan Priddis, editors |
| title_fullStr | Singularities, mirror symmetry, and the gauged linear sigma model Summer School, Crossing the walls in enumerative geoemetry, May 21 - June 1, 2018, Snowbird, Utah Tyler J. Jarvis, Nathan Priddis, editors |
| title_full_unstemmed | Singularities, mirror symmetry, and the gauged linear sigma model Summer School, Crossing the walls in enumerative geoemetry, May 21 - June 1, 2018, Snowbird, Utah Tyler J. Jarvis, Nathan Priddis, editors |
| title_short | Singularities, mirror symmetry, and the gauged linear sigma model |
| title_sort | singularities mirror symmetry and the gauged linear sigma model summer school crossing the walls in enumerative geoemetry may 21 june 1 2018 snowbird utah |
| title_sub | Summer School, Crossing the walls in enumerative geoemetry, May 21 - June 1, 2018, Snowbird, Utah |
| url | https://doi.org/10.1090/conm/763 |
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