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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Veröffentlicht in:Symmetry, Integrability and Geometry: Methods and Applications
Datum:2020
Hauptverfasser: Battistella, Luca, Carocci, Francesca, Manolache, Cristina
Format: Artikel
Sprache:English
Veröffentlicht: Інститут математики НАН України 2020
Online Zugang:https://nasplib.isofts.kiev.ua/handle/123456789/210584
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Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Zitieren: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
id nasplib_isofts_kiev_ua-123456789-210584
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
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
title Virtual Classes for the Working Mathematician
spellingShingle Virtual Classes for the Working Mathematician
Battistella, Luca
Carocci, Francesca
Manolache, Cristina
title_short 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_sort virtual classes for the working mathematician
author Battistella, Luca
Carocci, Francesca
Manolache, Cristina
author_facet Battistella, Luca
Carocci, Francesca
Manolache, Cristina
publishDate 2020
language English
container_title Symmetry, Integrability and Geometry: Methods and Applications
publisher Інститут математики НАН України
format Article
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.
issn 1815-0659
url https://nasplib.isofts.kiev.ua/handle/123456789/210584
citation_txt Virtual Classes for the Working Mathematician. Luca Battistella, Francesca Carocci and Cristina Manolache. SIGMA 16 (2020), 026, 38 pages
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