Hilbert Coefficients and Sally Modules: A Survey of Vasconcelos' Contributions

This paper surveys and summarizes Wolmer Vasconcelos’ results surrounding multiplicities, Hilbert coefficients, and their extensions. We particularly focus on Vasconcelos’ results regarding multiplicities and Chern coefficients, and other invariants which they bound. The Sally module is an important instrument introduced by Vasconcelos for this study, which naturally relates Hilbert coefficients to reduction numbers.