-
Topic: (transfer) Let me publish reference books on algebra and ryBrowsing: 925 related categories: Lixiaoxiangleon (author) 2010/1/22 top floor reportI learned algebra and ry .. I think algebra is much more interesting than differential ry. although the importance of sub- ry is unambiguous, there are more clever ideas and more interesting questions about algebra and ry .. 3 E * L7 K! Y (C2 x0 B2 E
To do something in the field of algebra, you need to learn the following skills: (difficult in books. (fun), from 1 to 5, from easy to difficult (boring to interesting) the return on investment will also be useful in the future if the market has read)
1 Wudang Changquan (basic effort), S + K/S 't8 L: G
Atiyah & McDonald's introduction to commutative algebra and Matsumura's commutative algebra are background knowledge of algebra in algebra. the two books only focus on algebra and do not mention ry, but the exercises in the first book have many good questions about the meaning behind ry. in fact, the theorem of any exchange Algebra has a geometric significance .; R & Y 'o1 Z3 L4 t D8 [
----------------- Difficult and interesting ** ROI **
2. yunqi (you can enter any branch after training ...)
The algebraic geometry of Robin Hartshorne is a classic textbook of algebraic ry. any less than fifty-year-old algebraic physicist grew up studying this book. this book is a very systematic summary of grothendick's attention and SGA. grothendick's book contains a complete set of contents, but is not practical: that is, the objects discussed are too common friends without geometric significance, which is not good at 01:10. however, the Hartshorne book makes the scheme program of grothendick the most appropriate interpretation. the exercises in this book are also very important, no matter the exercises in this book will always be useful for arithmetic or complex or more in-depth algebraic ry. #? @ * Q, D: K7 \ 7 A Z
-------------------- Difficult and interesting * ROI ***
(PS: the essence of Hartshorne's book is in Chapter 123, chapter 45 of which is useless for people who do not do arithmetic ry, and there is a better alternative to the book)
3 sets of martial arts costumes)
Gunning's lectures on Riann surface or Forster, Farkas, or Jost's Riann surface: The Cartesian surface is real mathematics. it has a major relationship with all mathematical points. the books of the above four authors are quite deep. I have read only gunning, a good book that attaches great importance to "same group transfer. other hyperbolic geometry, automorphism, or special linear series. they are all very interesting. many people, especially Chinese people, also like Wu hongxi's introduction to the Cartesian surface. but I do not like it very much. & c p! F2 V + G #_# j7 {-y *?
-------------------- Difficult and interesting **** 0 ROI
4 Basic internal skills of Quanzhen School (practice required)
The principles in algebraic geometry of Griffin & Haris. this book is classic. it is a basic textbook for complex ry. every chapter in this book is great. the first chapter is the Hodge theory .. it is the most profound theory in ry. in chapter 2, the embedding of kodaira embedding theorem is much more interesting than embedding of a real manifold. the third chapter is current and spectral sequence, which are very important tools. chapter 4 describes the surface theory. I wrote a lot of details but had a better book (see figure 6 ). the fifth special topic has different functions for people in different directions in kangaroo ry.
------------------- Difficult and interesting ***** ROI *****/g % N & L) S0 X1 M4 @
5 9 Yang Magic 3 L "L" F-} "W8 {+ E
The Compact complex surfaces of Barth & hulek & Peters. this book is a classic in classic. I am talking about various topics of algebraic surfaces. each chapter is infinitely perfect. it can be said that if you have never read this book in algebra and ry. I even learned a few boxes and never read this book .. line feed may be considered. it is a rare book for centuries. I personally think the last two new versions of this book are particularly good. one is the K3 surface, and the other is the doanaldson and seiber Witten theories. it is now an unlimited topic. * R6 H3 w6 M, e # J
------------------ Difficult and interesting * ROI * 7 O & @/a, H6 \ & U
6 Shaolin sect Luo Han Quan (you can practice it if it's okay)
Robert Friedman's Algebraic Surfaces and holomorphic vector bundles book is about the surface and the vector bundle above. the surface is a bit messy. In fact, no one talks about the surface better than Barth. you can see the value of the vector bundle. & X6 O: R5 y /{! Y
------------------ Difficult and interesting * ROI ** 0 o (n8 S7 U) J8 x
! W-H & Y: F $ P
7 star absorption method (after training, you can use the internal power of the differential extension scientist for your own use)/Q "W! F'n'/z) S4 x a "r j-x) i8 P # I
The geometry of four manifold of Donaldson & kroheim. this is the Bible in the differential extension. both of them are for everyone. this book introduces the gauge invariant (normative invariant) of four-dimensional manifold, and the complex surface is a category of four-dimensional manifold .. therefore, it is also a good book on algebra and ry. 9 N & F % r'l, {7 C-E9 \ 7 Z! T
------------------ Difficult and interesting **** ROI 0 (50 years later), o8 w-D.]/R0 V0 D "F: Q
8. Qian Kun moved the game to another place. (If you get half done, you will have enough strength. After all the exercises are completed, you will also vomit blood and die.) 2 V3 Q (K5 H-P1 _ & D9 G7 {! V1 V9 J
John Morgan and Robert Friedman's smooth four manifold and complex surfaces... k! A3 d' R (}
This book is about elliptical surfaces and the theory of norm invariant of Donaldson. by using this theory, the author obtains a big theorem of a curved surface, proving that only a limited number of complex deformation classes can share one differential structure at most. I am still studying hard.
------------------------ Difficult and interesting ***** ROI **;? 4 F $ _ 3 e $ s/o
9. The Invincible firewheel of muscle meat and Garfield (think twice before training)
The geometry of algebraic crves of Haris. it is a very narrow field. we are studying special linear systems on algebraic curves. A very difficult book. it is of little use after reading it .. but it can become an expert in algebraic curves ., d; Z4 U "I (Y1 I9 O (j9 E: C3 W" C
------------------------ Difficult and interesting * ROI **. G: @ & R; W. B3 C * S2 U + F2 Z4 W
10 five-year-old swordsman (useful but rather messy)
The moduli of curves of Joe Harris & David Morrison is a classic of the curve-based model space. but I don't like it that much. there is an introduction to Enumerative geometry. there are intersection numbers and various properties in the curve space. -"[) | $ C % L $ G2 \ * x % P1 V, Q6 y0 T5
----------------------- Difficult and interesting ** ROI *****
11. jiuyin Zhenjing (after training, you can start to study problems)
John Morgan and Robert Friedman's gauge theory and the topology of Four-manifolds. there is gieseker's theory of geometric invariant writing. comparison theorem of Uhlenbeck closeness and gesieker closeness of Li Jun. morgan discusses Donaldson's normative constants and the computing results of more people. ------------------------- Difficult and interesting ****** ROI *****
12 Taijiquan (unlimited development)
The geoemtry of moduli space of sheaves.: C "}: F & K (N: V8 ~ // @ & I # I
It is a classic usage of vector clustering space. the second part has the most advanced results of this discipline. the appendix of each chapter has important and interesting results. -y * |-S & X/K8 o z: S
------------------------ Difficulty and difficulty * ROI * 7 K + _) F "F (W W2 s" e/m
13 mk47 rifle (can deal with Level 1 martial arts experts) ${2 W-R: M8] % Y! O. K
Joyce, gross & huybrecht's Calabi-Yau manifolds and related geometries. is the latest special book about mirror wannry. describes the problems related to the Calabi Yau manifold. an overview of how Yau solves Calabi conjecture. there are mirror conjecture and syz (Strominger & Yau & zaslow) conjecture. we also discuss the nature of hyperkaeler manifold. this is the mathematics of the 20th century. 4 {2 {L. p4 P & H #[2 S + \ $ X, c
-------------------- Difficult and interesting ****** ROI *****/Q % M $ I '_. Z "Q
14 Machine Gun (can rob banks)-C. @. E5 U "m3 [. W; K2 x9 y) u2 t
Pandharipande, Sheldon Katz, Hori... A group of people write the mirror into ry. in addition to the proof of mirror conjecture in quintic three fold, it also includes the gopakuma Vafa conjecture, homological mirror wannry conjecture, and even the source of mirror wannry: the string theory and the Field Theory in high-energy physics are all written by experts .. from hard to easy .. I am also in closed training.: E9 J6 C & '5 {'z
----------- Difficult (physical) Interesting ******* ROI ****** 7x6 H7 A8 '#
15 atomic bombs (...................)
The topics in trascendental geometry of Griffin is a classic book of the Hodge structure. in around 1985, there was a large number of mathematicians who wanted to solve huochi's Conjecture (that's right, the 1 million problem ). although they did not understand it, they had a deep understanding of the conjecture. this is a brief description of their work. it is a book that is hard to read but worth reading.
Difficult and interesting ***************** **
There are several other books not introduced .. for example, the minimal model Programm of the third of Mori is a complex manifold .. however, this problem has been solved by Tom and four other foreigners (in all dimensions), and the return on investment has been negative. or
Transferred from:
2 B? (}! D8 D4 V + O9 T $}: E3 u
PhD mathematical Forum quillen
5 L7 [6 Q! Y-[U % K + {4 Z! U
I know many people who read Hartshorne in college, and even some girls. But after I met so many mathematical workers, I found that such a person is not the best. Really cool people are people who can read general nature from special examples It is interesting to use algebra. however, students have many different backgrounds. for example, the analysis of the person reading the Hartshorne is not necessarily good. The person reading the Hartshorne is not necessarily good .. hartshorne does not follow the rule. both of them can be used, but they are not necessarily the same. the main reason is that the complex ry is very different from the pure algebraic ry. In the complex ry, classical cohomology or homotopy does not require special processing, in the case that scheme over K and K is not the plural body (many people care about the finite body) classical cohomology requires an entire SGA to define
For etale cohomology and homotopy, use Motivic homotopic theory. & F-r-u * T9 P0 K of voevosky/Levine.
Not to mention the famous Hodge decompsition, harmonic analysis, or connection (specification) on holomorphic bundle, which is only available in complex ry and not much in algebraic ry. 2 U3 X8 Q7 h) y ++ ~ I personally think that complex ry is more valuable than pure algebra ry. it is mainly intuitive to provide. intuition is not easy to generate. In many cases, algebra is just a simple tool for discussing objects, which is not the same as objects themselves. however, it cannot be ignored. it should only be intuitive and use algebra (analysis can also be used ). of course, it will be very useful to learn extremely high level algebra. in addition, algebra is a beautiful way to simplify the analysis language. for example, Chapter 1 of Hartshorne is. but it should not be lost in beautiful languages. after all, you can't do anything you can ., q (n, B '~ 9 r Two benefits of Hartshorne are that they do not exist in the complex ry. first, except that K is not a complex variety (or scheme), and second, it is a tool for studying singularity. or, rather, language. although it is just a language, it is almost impossible to study singularity in analysis. After assuming that it is a Polynomial Type singularity, the exchange algebra can be performed on stage. so there is a famous saying: algebra is just a finite-dimensional analysis.
6 I + k {4 O + x $ T9 t; q-B1 d
Of course, I mentioned the general theory above. In the algebraic ry, the algebraic curve = the Cartesian surface = Yes
A constant curvature gauge manifold. This one-dimensional (real two-dimensional) situation is the intersection of all disciplines. There is no better learning difference from any other direction. |
