Virtual classes for the working mathematician
Luca Battistella, Francesca Carocci, Cristina Manolache

TL;DR
This paper provides an accessible introduction to virtual classes in algebraic geometry, discussing their properties, applications, and including new theorems and computations in simple cases.
Contribution
It offers a comprehensive review of virtual classes, introduces a new virtual push-forward theorem, and demonstrates computations through simple examples.
Findings
Introduction of a new virtual push-forward theorem
Computation of virtual classes in basic examples
Summary of properties and applications of virtual classes
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.
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