Virtual Classes for the Working Mathematician
This note is intended to be a friendly introduction to virtual classes. We review virtual classes, and we give a number of properties and applications. We also include a new virtual push-forward theorem and many computations of virtual classes in simple examples.
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2020 |
| Main Authors: | , , |
| 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/123456789/210584 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Virtual Classes for the Working Mathematician. Luca Battistella, Francesca Carocci and Cristina Manolache. SIGMA 16 (2020), 026, 38 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862620905938616320 |
|---|---|
| author | Battistella, Luca Carocci, Francesca Manolache, Cristina |
| author_facet | Battistella, Luca Carocci, Francesca Manolache, Cristina |
| citation_txt | Virtual Classes for the Working Mathematician. Luca Battistella, Francesca Carocci and Cristina Manolache. SIGMA 16 (2020), 026, 38 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | This note is intended to be a friendly introduction to virtual classes. We review virtual classes, and we give a number of properties and applications. We also include a new virtual push-forward theorem and many computations of virtual classes in simple examples.
|
| first_indexed | 2025-12-17T12:04:17Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-210584 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-17T12:04:17Z |
| publishDate | 2020 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Battistella, Luca Carocci, Francesca Manolache, Cristina 2025-12-12T10:30:05Z 2020 Virtual Classes for the Working Mathematician. Luca Battistella, Francesca Carocci and Cristina Manolache. SIGMA 16 (2020), 026, 38 pages 1815-0659 2020 Mathematics Subject Classification: 14C17; 14N35; 14D23 arXiv:1804.06048 https://nasplib.isofts.kiev.ua/handle/123456789/210584 https://doi.org/10.3842/SIGMA.2020.026 This note is intended to be a friendly introduction to virtual classes. We review virtual classes, and we give a number of properties and applications. We also include a new virtual push-forward theorem and many computations of virtual classes in simple examples. Most of the material presented here was presented at the Summer School in Enumerative Geometry at SISSA, Trieste, in 2017. A shorter version was part of a Lecture series within the Workshop on Moduli and Mirror Symmetry held by C.M. in Alpensia in 2016. We thank the organisers of these schools for the invitation and the wonderful work environment. We would also like to thank the participants for their interest in the material in this note grew to answer the questions asked during these workshops. We thank Tom Coates for comments on the manuscript. We also thank the referees for their attentive remarks. L.B. was supported by a Royal Society 1st Year URF and DHF Research Grant Scheme. C.M. is supported by an EPSRC-funded Royal Society Dorothy Hodgkin Fellowship. This work was supported by the Engineering and Physical Sciences Research Council grant EP/L015234/1: the EPSRC Centre for Doctoral Training in Geometry and Number Theory at the Interface. This note was finished while L.B. and C.M. were in residence at the Mathematical Sciences Research Institute in Berkeley, California, during the Spring 2018 semester, and it is supported by the National Science Foundation under Grant No. DMS-1440140. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Virtual Classes for the Working Mathematician Article published earlier |
| spellingShingle | Virtual Classes for the Working Mathematician Battistella, Luca Carocci, Francesca Manolache, Cristina |
| title | Virtual Classes for the Working Mathematician |
| title_full | Virtual Classes for the Working Mathematician |
| title_fullStr | Virtual Classes for the Working Mathematician |
| title_full_unstemmed | Virtual Classes for the Working Mathematician |
| title_short | Virtual Classes for the Working Mathematician |
| title_sort | virtual classes for the working mathematician |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/210584 |
| work_keys_str_mv | AT battistellaluca virtualclassesfortheworkingmathematician AT caroccifrancesca virtualclassesfortheworkingmathematician AT manolachecristina virtualclassesfortheworkingmathematician |