Methods of Algebraic Geometry: Volume 1

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Cambridge University Press, 10 mars 1994 - 452 pages
All three volumes of Hodge and Pedoe's classic work have now been reissued. Together, these books give an insight into algebraic geometry that is unique and unsurpassed.
 

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Table des matières

RINGS AND FIELDS
1
1Groups
2
2Rings
6
3Classification of rings
12
4The quotient field of an Integral domain
15
5Polynomial rings
19
6The division algorithm
24
7Factorisation in an integral domain
27
6Desargues Theorem
191
7Some fundamental constructions
196
8The condition for a commutative field Pappus Theorem
202
9Some finite geometries
205
10rway spaces
206
PROJECTIVE SPACE SYNTHETIC DEFINITION
208
2Desargues Theorem
213
3Related ranges
216

8Factorisation in polynomial rings
33
9Examples of fields
37
LINEAR ALGEBRA MATRICES DETERMINANTS
41
2Matrices
49
4Transformations of a matrix
58
5The rank of a matrix
65
6Homogeneous linear equations
68
7Matrices over a commutative field
71
8Determinants
73
9Xmatrices
86
10Miscellaneous theorems
95
CHAPTER III ALGEBRAIC DEPENDENCE
99
2Extensions of a commutative field
101
3Extensions of finite degree
105
4Factorisation of polynomials
111
5Differentiation of polynomials
119
6Primitive elements of algebraic extensions
126
7Differentiation of algebraic functions
128
8Some useful theorems
136
ALGEBRAIC EQUATIONS
139
2Hilberts basis theorem
142
3The resultant of two binary forms
146
4Some properties of the resultant
152
6The resultant system for a set of homogeneous equations in several unknowns
159
7Nonhomogeneous equations in several unknowns
162
8Hilberts zerotheorem
165
9The resultant ideal
166
10The uresultant of a system of equations
171
BOOK II PROJECTIVE SPACE
175
2Projective number space
176
3Projective space of n dimensions
178
4Linear dependence in PnK
180
5Equations of linear spaces
186
4Harmonic conjugates
224
5Two projectively invariant constructions
231
6Reference systems
246
7The algebra of points on a line
253
8The representation of the incidence space as a PnK
259
9Restrictions on the geometry
272
10Consequences of assuming Pappus Theorem
274
GRASSMANN COORDINATES
286
2Grassmann coordinates
288
3Dual Grassmann coordinates
292
4Elementary properties of Grassmann coordinates
297
5Some results on intersections and joins
304
6Quadratic prelations
309
7The basis theorem
315
COLLINEATIONS
322
2Collineations
327
3United points and primes of a nonsingular collineation
333
4The united kspaces of a nonsingular collineation
344
5Cyclic collineations
352
6Some particular collineations
354
7Singular collineations
358
CORRELATIONS
362
2Polarities
367
3Nullpolarities
378
4Simple correlations
390
5Transformation of the general correlation
395
6Canonical forms for correlations
411
7Some geometrical properties of correlations
419
BIBLIOGRAPHICAL NOTES
430
BIBLIOGRAPHY
431
INDEX
433
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