Discussion Overview
The discussion centers around recommendations for books and references related to the study of singular points of algebraic curves within the field of algebraic geometry. Participants share their experiences and suggest various texts that cover general methods, classifications, and specific treatments of singular points.
Discussion Character
- Exploratory
- Technical explanation
- Debate/contested
Main Points Raised
- One participant expresses a desire to explore singular points of algebraic curves and seeks recommendations for self-study materials.
- Another participant recommends Robert J. Walker's "Algebraic Curves" as a helpful starting point, particularly chapter 3.
- Additional references suggested include Shafarevich's "Basic Algebraic Geometry," Milnor's "Singularities of Complex Hypersurfaces," and Laufer's work on two-dimensional singularities.
- Greuel, Lossen, and Shustin's "Introduction to Singularities and Deformations" is mentioned for its useful insights, especially regarding Milnor's results.
- Arnol’d, Gusein-Zade, and Varchenko's "Singularities of Differentiable Maps" is noted for its summaries of relevant results.
- A participant mentions C.T.C. Wall's "Singular Points of Plane Curves" as a comprehensive treatment, though it is noted to be expensive.
Areas of Agreement / Disagreement
Participants generally agree on the usefulness of Walker's book as a starting point, but there are multiple competing views regarding the best resources, with no consensus on a single definitive text.
Contextual Notes
Some participants have not fully explored all suggested texts, indicating that their recommendations are based on limited experience with the materials. There may be varying levels of depth and focus in the suggested books, which could affect their suitability for different readers.
Who May Find This Useful
This discussion may be useful for graduate students or researchers interested in algebraic geometry, particularly those focusing on singular points of algebraic curves.