Hilbert coefficients and Sally modules: a survey of Vasconcelos’ contributions
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Jooyoun Hong
Abstract
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.
Abstract
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.
Chapters in this book
- Frontmatter I
- Preface V
- Contents VII
- Wolmer Vasconcelos, a tribute IX
- Vasconcelos Bibliography (1964–2024) XVII
- The early years: flatness, projectivity, and R-sequences 1
- Joint work with Wolmer Vasconcelos. The early years 41
- Homological properties of the module of differentials 71
- Hilbert coefficients and Sally modules: a survey of Vasconcelos’ contributions 97
- Graph rings and ideals: Wolmer Vasconcelos’ contributions 133
- Degrees: Vasconcelos contributions 203
- The books of Wolmer V. Vasconcelos 241
- Finding nilpotents with Wolmer Vasconcelos 261
- Rees algebras over residual intersections 279
- Structure theorems for Gorenstein ideals of codimension four with small number of generators 297
- Sifted degrees of the equations of the Rees module and their connection with the Artin–Rees numbers 333
- Reembeddings of special border basis schemes 353
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- Rings with q-torsionfree canonical modules 405
Chapters in this book
- Frontmatter I
- Preface V
- Contents VII
- Wolmer Vasconcelos, a tribute IX
- Vasconcelos Bibliography (1964–2024) XVII
- The early years: flatness, projectivity, and R-sequences 1
- Joint work with Wolmer Vasconcelos. The early years 41
- Homological properties of the module of differentials 71
- Hilbert coefficients and Sally modules: a survey of Vasconcelos’ contributions 97
- Graph rings and ideals: Wolmer Vasconcelos’ contributions 133
- Degrees: Vasconcelos contributions 203
- The books of Wolmer V. Vasconcelos 241
- Finding nilpotents with Wolmer Vasconcelos 261
- Rees algebras over residual intersections 279
- Structure theorems for Gorenstein ideals of codimension four with small number of generators 297
- Sifted degrees of the equations of the Rees module and their connection with the Artin–Rees numbers 333
- Reembeddings of special border basis schemes 353
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- Rings with q-torsionfree canonical modules 405
