Book recommendations about singular points of algebraic curves

AI Thread Summary
The discussion focuses on book recommendations for studying singular points of algebraic curves in algebraic geometry. Key suggestions include Robert J. Walker's "Algebraic Curves" as a foundational text, along with Shafarevich's "Basic Algebraic Geometry" and Milnor's "Singularities of Complex Hypersurfaces." Additional resources mentioned are "Introduction to Singularities and Deformations" by Greuel, Lossen, and Shustin, and "Singularities of Differentiable Maps" by Arnol’d, Gusein-Zade, and Varchenko. C.T.C. Wall's work on singular points of plane curves is also noted as a comprehensive but more expensive option. These texts collectively provide a solid starting point for self-study in the subject.
V9999
Messages
17
Reaction score
3
I'm not quite sure if this is an appropriate question in this forum, but here is the situation.

I have just finished my graduate studies. Now, I want to explore algebraic geometry. Precisely, I am interested in the following topics:
Singular points of algebraic curves;
General methods employed to determine the singular points of algebraic curves;
Classification of singular points of algebraic curves;

Based on your experience, what are the best books/references for self-study on those topics?
 
Physics news on Phys.org
I know only a little about singular points, but I myself began first to have some grasp of them by reading chapter 3 of the well written and precise little book by Robert J. Walker, Algebraic Curves. Here is a cheap used copy:
https://www.abebooks.com/9780486603360/Algebraic-Curves-Walker-Robert-J-0486603369/plp

this one helped me personally the most. The others I have on my shelf are:

Shafarevich, Basic Algebraic Geometry, vol. I, 2nd edition, chapter IV.4.

I have not read the following as much, but hope to some day:

The wonderful book by Milnor: Singularities of complex hypersurfaces,
https://www.amazon.com/dp/0691080658/?tag=pfamazon01-20

and for surfaces only: Normal; two dimensional singularities, by Henry Laufer. (I have never gotten into this, but he is an expert.)

I have dipped into this next one with good results, especially (I think) its accounts of Milnor's results:
Introduction to singularities and deformations, by Greuel, Lossen and Shustin.

Another excellent one whose summaries of results have helped me is:
V. Arnol’d, S. Gusein-Zade, A. Varchenko, Singularities of Differentiable Maps,
vol.I, Monographs in Mathematics, Birkh¨auser, 1985.

So to get started, I suggest Walker. Oh yes, and you might take a look at chapter 3 of Plane algebraic curves, by Brieskorn and Knorrer. and the Shafarevich reference above.
 
Last edited:
mathwonk said:
I know only a little about singular points, but I myself began first to have some grasp of them by reading chapter 3 of the well written and precise little book by Robert J. Walker, Algebraic Curves. Here is a cheap used copy:
https://www.abebooks.com/9780486603360/Algebraic-Curves-Walker-Robert-J-0486603369/plp

this one helped me personally the most. The others I have on my shelf are:

Shafarevich, Basic Algebraic Geometry, vol. I, 2nd edition, chapter IV.4.

I have not read the following as much, but hope to some day:

The wonderful book by Milnor: Singularities of complex hypersurfaces,
https://www.amazon.com/dp/0691080658/?tag=pfamazon01-20

and for surfaces only: Normal; two dimensional singularities, by Henry Laufer. (I have never gotten into this, but he is an expert.)

I have dipped into this next one with good results, especially (I think) its accounts of Milnor's results:
Introduction to singularities and deformations, by Greuel, Lossen and Shustin.

Another excellent one whose summaries of results have helped me is:
V. Arnol’d, S. Gusein-Zade, A. Varchenko, Singularities of Differentiable Maps,
vol.I, Monographs in Mathematics, Birkh¨auser, 1985.

So to get started, I suggest Walker. Oh yes, and you might take a look at chapter 3 of Plane algebraic curves, by Brieskorn and Knorrer. and Shafarevich.
Many, many thanks for the suggestions!
 
ok here is a comprehensive treatment by an expert, of the full range of ideas involved in studying singular points of plane curves. Unfortunately it is not cheap. I also have a (used) copy of this on my shelf and it looks quite promising, but I have not read it much yet. Singular points of plane curves, by C.T.C.Wall:
at least there is an affordable ecopy available and a used copy at half the exhorbitant new price: it should also be available in libraries. I would still start with Walker.

https://www.amazon.com/dp/0521839041/?tag=pfamazon01-20
 
Last edited:
The book is fascinating. If your education includes a typical math degree curriculum, with Lebesgue integration, functional analysis, etc, it teaches QFT with only a passing acquaintance of ordinary QM you would get at HS. However, I would read Lenny Susskind's book on QM first. Purchased a copy straight away, but it will not arrive until the end of December; however, Scribd has a PDF I am now studying. The first part introduces distribution theory (and other related concepts), which...

Similar threads

Replies
9
Views
4K
Replies
8
Views
198
Replies
6
Views
3K
Replies
5
Views
4K
Replies
5
Views
4K
Back
Top