Virtual classes for the working mathematician

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.