Virtual classes for the working mathematician

2018/04/30 by Mathematikon, Germany, Luca Battistella, Luca Battistell +4 · 1 citation
Computer Science · Mathematics · #Algebra over a field #Algebraic Geometry and Number Theory #Computation #Computer science #Epistemology #Geometric and Algebraic Topology #Mathematics #Polynomial and algebraic computation #Programming language #Pure mathematics #Simple (philosophy) #Theoretical computer science #math.AG

paper · pdf · doi:10.3842/sigma.2020.026

published as SIGMA 16 (2020), 026, 38 pages

openalex created_date 2018/04/24 · arxiv created 2020/04/09 · openalex publication_date 2020/04/09 · arxiv updated 2020/04/13 · openalex updated_date 2026/08/05

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.

Citations

• 13/2 ways of counting curves
• A splitting of the virtual class for genus one stable maps
• Intersection Theory

Cited by

• Normal cone (algebraic geometry) [wikipedia]

Related

• Virtual Calculus - Part II
• Constructing virtual Euler cycles and classes
• Virtual classes for hypersurfaces via two-periodic complexes
• Virtual Calculus - Part I
• Virtual pullbacks in K-theory