Higher-Dimensional Algebraic GeometrySpringer Science & Business Media, 26 июн. 2001 г. - Всего страниц: 234 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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III | 5 |
IV | 6 |
V | 8 |
VI | 14 |
VII | 17 |
VIII | 18 |
IX | 20 |
X | 23 |
XLIII | 115 |
XLV | 117 |
XLVI | 120 |
XLVII | 124 |
XLVIII | 126 |
XLIX | 131 |
L | 134 |
LI | 135 |
XI | 25 |
XII | 27 |
XIII | 31 |
XIV | 33 |
XV | 39 |
XVI | 41 |
XVIII | 42 |
XIX | 43 |
XX | 49 |
XXI | 51 |
XXII | 56 |
XXIII | 59 |
XXV | 60 |
XXVI | 64 |
XXVII | 67 |
XXVIII | 70 |
XXIX | 74 |
XXX | 77 |
XXXI | 80 |
XXXII | 83 |
XXXIII | 84 |
XXXIV | 88 |
XXXV | 89 |
XXXVI | 90 |
XXXVII | 93 |
XXXVIII | 100 |
XXXIX | 103 |
XL | 104 |
XLI | 108 |
XLII | 112 |
LII | 137 |
LIII | 138 |
LIV | 140 |
LV | 141 |
LVI | 145 |
LVII | 147 |
LIX | 148 |
LX | 149 |
LXI | 153 |
LXII | 155 |
LXIII | 158 |
LXIV | 161 |
LXV | 168 |
LXVI | 171 |
LXVIII | 174 |
LXIX | 178 |
LXX | 186 |
LXXI | 188 |
LXXII | 190 |
LXXIII | 192 |
LXXIV | 198 |
LXXV | 201 |
LXXVI | 206 |
LXXVII | 209 |
LXXVIII | 214 |
LXXIX | 218 |
225 | |
233 | |
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Часто встречающиеся слова и выражения
abelian variety algebraically closed ample divisor Assume base-point-free blow-up canonical divisor canonical singularities Cartier divisor characteristic zero closure codimension codimension at least coefficients coherent sheaf cone theorem construction contained contraction Corollary curve f D₁ defined degree dense open subset desingularization dim(X dimension effective divisor exact sequence exceptional divisor exceptional locus exists f*Tx Fano variety fiber finite follows free rational curve Geometry hence hyperplane hypersurface implies irreducible component irreducible curve isomorphic let f minimal model Mor(C Mor(P¹ Mor(Y Mori's NE(X nef and big nef divisor nonnegative nonzero normal bundle open subset parametrized Picard number polynomial positive integer projective variety proof proper proper morphism Proposition prove Q-factorial quasi-projective rational map rationally chain-connected scheme sheaf simple normal crossings smooth projective variety smooth variety subscheme subvariety sufficiently large surjective tangent uniruled vanishing theorem variety and let vector bundle Xfree
Популярные отрывки
Стр. 223 - J.-P. Demailly, A numerical criterion for very ample line bundles, J.
Стр. 223 - Ekedahl T., Canonical models of surfaces of general type in positive characteristic, Publ.