Higher-Dimensional Algebraic Geometry

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Springer Science & Business Media, Jun 26, 2001 - Mathematics - 234 pages
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Higher-dimensional algebraic geometry studies the classification theory of algebraic varieties. This very active area of research is still developing, but an amazing quantity of knowledge has accumulated over the past twenty years. The author¿s goal is to provide an easily accessible introduction to the subject. The book covers preparatory and standard definitions and results, moves on to discuss various aspects of the geometry of smooth projective varieties with many rational curves, and finishes in taking the first steps towards Mori¿s minimal model program of classification of algebraic varieties by proving the cone and contraction theorems. The book is well organized and the author has kept the number of concepts that are used but not proved to a minimum to provide a mostly self-contained introduction to graduate students and researchers.
 

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Contents

III
1
IV
2
V
4
VI
10
VII
13
VIII
14
IX
16
X
19
XLII
111
XLIII
113
XLIV
116
XLV
120
XLVI
122
XLVII
127
XLVIII
130
XLIX
131

XI
21
XII
23
XIII
27
XIV
29
XV
35
XVI
37
XVII
38
XVIII
39
XIX
45
XX
47
XXI
52
XXII
55
XXIII
56
XXIV
60
XXV
63
XXVI
66
XXVII
70
XXVIII
73
XXIX
76
XXX
79
XXXI
80
XXXII
84
XXXIII
85
XXXIV
86
XXXV
89
XXXVI
96
XXXVII
99
XXXIX
100
XL
104
XLI
108
L
133
LI
134
LII
136
LIII
137
LIV
141
LV
143
LVI
144
LVII
145
LVIII
149
LIX
151
LX
154
LXI
157
LXII
164
LXIII
167
LXIV
170
LXV
174
LXVI
182
LXVII
184
LXVIII
186
LXIX
188
LXX
194
LXXI
197
LXXII
202
LXXIII
205
LXXIV
210
LXXV
214
LXXVI
221
LXXVII
229
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Page 221 - Kawamata. Y., A generalization of Kodaira-Ramanujam's vanishing theorem, Math. Ann. 261 (1982), 43-46.
Page 221 - Kawamata, Y., Minimal models and the Kodaira dimension of algebraic fiber spaces.

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