Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 16 (2020), 026, 38 pages      arXiv:1804.06048      https://doi.org/10.3842/SIGMA.2020.026
Contribution to the Special Issue on Integrability, Geometry, Moduli in honor of Motohico Mulase for his 65th birthday

Virtual Classes for the Working Mathematician

Luca Battistella a, Francesca Carocci b and Cristina Manolache c
a) Mathematikon, Im Neuenheimer Feld 205, 69120 Heidelberg, Germany
b) JCMB, Peter Guthrie Tait Road, Edinburgh EH9 3FD, UK
c) Hicks building, 226 Hounsfield Rd, Broomhall, Sheffield S3 7RH, UK

Received October 03, 2019, in final form March 25, 2020; Published online April 09, 2020

Abstract
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.

Key words: intersection theory; virtual classes; Gromov-Witten theory; moduli spaces.

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