Virtual classes for the working mathematician
arXiv:1804.06048 · doi:10.3842/SIGMA.2020.026
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.
References in corpus (14)
- Curve counting via stable pairs in the derived category
- Gromov-Witten invariants in algebraic geometry
- Cycle groups for Artin stacks
- Moduli stacks of stable toric quasimaps
- Computing characteristic classes of projective schemes
- Standard vs. Reduced Genus-One Gromov-Witten Invariants
- 13/2 ways of counting curves
- An Algorithm to Compute the Topological Euler Characteristic, Chern-Schwartz-MacPherson Class and Segre Class of Projective Varieties
- The Quantum Lefschetz Hyperplane Principle Can Fail for Positive Orbifold Hypersurfaces
- Segre classes as integrals over polytopes
- Interpolation of characteristic classes of singular hypersurfaces
- A Direct Algorithm to Compute the Topological Euler Characteristic and Chern-Schwartz-MacPherson Class of Projective Complete Intersection Varieties
- A splitting of the virtual class for genus one stable maps
- Segre Classes on Smooth Projective Toric Varieties