Kollar J., Mori S. — Birational geometry of algebraic varieties :: Электронная библиотека попечительского совета мехмата МГУ

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Kollar J., Mori S. — Birational geometry of algebraic varieties

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Название: Birational geometry of algebraic varieties

Авторы: Kollar J., Mori S.

Аннотация:

One of the major discoveries of the past two decades in algebraic geometry is the realization that the theory of minimal models of surfaces can be generalized to higher dimensional varieties. This generalization, called the minimal model program, or Mori's program, has developed into a powerful tool with applications to diverse questions in algebraic geometry and beyond. This book provides the first comprehensive introduction to the circle of ideas developed around the program, the prerequisites being only a basic knowledge of algebraic geometry. It will be of great interest to graduate students and researchers working in algebraic geometry and related fields.

Язык:

Рубрика: Математика/Алгебра/Алгебраическая геометрия/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1998

Количество страниц: 254

Добавлена в каталог: 16.03.2005

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Предметный указатель

Hodge index theorem      11 21
Hodge theory      63
Horizontal      208
Hurwitz formula      210
Implicit function theorem      148
In codimension      159
Indeterminacy      8 11
Index 1 cover      159
Index of a divisor      159
Index of a variety      159
Intersection, number      29
Inversion of adjunction      173 174
Kahler manifold      13
Kawamata log terminal, kit      56
Kit, Kawamata log terminal      56
Kleiman’s criterion      19 33 35
Kodaira dimension      237
Kodaira vanishing theorem      62 70
Kodaira vanishing, general      73
Kodaira’s canonical bundle formula      49
Lattice bundle      10 /
Lc, log canonical      56
Lc, log canonical morphism      208
Lemma, Chow’s      32
Lemma, Hensel’s      125
Lemma, rigidity      9
Leray spectral sequence      3 71 73 156 162 185
Linear equivalence      4
Linear f-equivalence      5
Locally analytically $\mathbb{Q}$ -factorial      47
Log canonical, lc      56
Log canonical, lc, morphism      208
Log canonical, lc, numerically      112
Log canonical, lc, semi, sic      209
Log resolution      3 5 58
Log terminal, It      57
Log variety      48
Lt, log terminal      57
Luroth’s theorem      8
Manifold, compact complex      13
Manifold, Kahler      13
MAP      4
Map, bimeromorphic      6
Map, birational      6
Map, meromorphic      6
Map, rational      5
Meromorphic map      6
Minimal embedding      150
Minimal f-      106
Minimal model      vii 27 43 44 46 107
Minimal model, G-      48
Minimal model, program      vii 43 98
Minimal relatively      106
Minimal variety      43
Miniversal deformation      145
MMP      43 98
MMP, over S      98
MMP, semi-stable      208
Model, canonical      107
Model, G-minimal      48
Model, minimal      27 43 44 107
Model, weak canonical      107
Mori’s program, vii      43
Morphism      4
Morphism, contraction      27
Morphism, divisorial log terminal, dlt      208
Morphism, Frobenius      13 14 16
Morphism, log canonical, lc      208
Multiple curve      11
Multiple curve, $\mu_r$ , the group of r-th-roots of 1      171
Multiple curve, $\mu_{\infty}$ , the group of roots of 1      217
Nakai — Moishezon criterion      31 34
NE(X), the cone of curves $\subset N_1(X)$       19
NE(X/Y)      45 95
Nef      4 35
Nef, divisors, example of /-      35
Nef, f-      35
Neron — Severi      11 19
Neron — Severi group      11 19
Neron — Severi theorem of the base of      19
Non-vanishing theorem      75 91
Norm      154
NS(X), the Neron — Severi group of X      19
Number, intersection      29
Numerical equivalence      4 18
Numerical f-equivalence      5
Numerically dlt      112
Numerically log canonical      112
Numerically trivial      4
Of pure codimension      8 70
One-parameter family      13
Open condition      122
Open variety      49
Picard number      19
Picard number, relative      45
Pit, purely log terminal      56
Prime divisor      4
Principle, GAGA      62
Pull back of a Weil divisor      160
Purely log terminal, pit      56
Quasi-finite      149 150
Quotient singularity      158
Ramified cyclic cover      64
Rational map      5
Rational resolution      155
Rational singularity      155
Rationality theorem      75 86
Ray, extremal      18
redX, the maximal reduced closed subscheme of X      5
Regular function      148
Regular sequence      153
Relative, 1-cycle      45
Relative, basepoint-free theorem      94
Relative, cone theorem      95
Relative, minimal model program      98
Relative, Picard number      45

Relative, trace map      185
Relatively minimal      106
Relativization      45
Resolution      3 5
Resolution for a divisor      61
Resolution for kit pair      58
Resolution with $f^{-1}\Delta$ smooth      55
Resolution, log      3 5 58
Resolution, rational      155
Resolution, semi-stable      235
Resolution, simultaneous      128 234
Riemann — Roch theorem      20 30
Rigidity lemma      9
Ring, canonical      80 237
Round down, $\lfloor\rfloor$       5
Round up, $\lceil\rceil$       5
Ruled surface      21
Semi log canonical, sic      209
Semi-stable flip      viii
Semi-stable MMP      208
Semi-stable reduction theorem      214 215 228 232
Semi-stable resolution      235
Sequence of flips      193
Sequence of flops      194
Sequence, Leray spectral      3 71 73 156 162 185
Sequence, regular      153
Serre duality      72 163 182
Serre vanishing theorem      66
Sic, semi log canonical      209
Simple elliptic      116
Simple normal crossing divisor, snc      5
Simple singularity      122
Simultaneous Resolution      128 234
Singularity, analytic type      193
Singularity, canonical      42
Singularity, Du Val      143 165
Singularity, quotient      158
Singularity, simple      122
Singularity, surface quotient      viii
Singularity, terminal      42 46 199
Small contraction      38
Snc, simple normal crossing      5
Space, deformation      12 232
Space, Fano fiber      44
Spectral sequence, Leray      3 71 73 156 162 185
Stable curve      230
Standard terminalization      195 215
Stein factorization      150
Subcone, extremal      18
SuppD, support of divisor D      4
Surface, abelian      22
Surface, analytic      25
Surface, cubic      22
Surface, Del Pezzo      22 39
Surface, quotient singularity      viii
Surface, ruled      21
Symbolic blow up      199
Symbolic power algebra      189
Terminal      42 56
Terminal, flop      191 192
Terminal, singularity      42 46 199
Terminalization      195
Terminalization, standard      195 215
Termination of flips      193 210 211
Termination of flops      194 203 205
Theorem of the base of Neron — Severi      19
Theorem, basepoint-free      75 78
Theorem, Castelnuovo’s      8
Theorem, cone      22 27 38 43 76 81
Theorem, contraction      76
Theorem, easy termination      203
Theorem, Hironaka      3 4
Theorem, Hodge index      11 21
Theorem, implicit function      148
Theorem, Kodaira vanishing      62 70
Theorem, Luroth’s      8
Theorem, non-vanishing      75 91
Theorem, rationality      75 86
Theorem, relative basepoint-free      94
Theorem, relative cone      95
Theorem, Riemann — Roch      20
Theorem, semi-stable reduction      214 215 228 232
Theorem, weak Hironaka      3 4
Theorem, Weierstrass preparation      125
Theory, deformation      12
Theory, elimination      15
Theory, Hodge      63
Total discrepancy      52
totaldiscrep(X, $\Delta$ )      52
Trace      154
Trace, relative      185
Transform, birational      5
TREE      114
Trivial      4
Trivial, numerically      4
Tyurina number, $\tau(X)$       129
Unbranched cover      13
Unramifled cyclic cover      63
Valuation, algebraic      50
Vanishing theorem, general Kodaira      73
Vanishing theorem, Kodaira      62 70
Vanishing theorem, Serre      66
Variety, log      48
Variety, minimal      43
Variety, open      49
Variety, Pano      28
Versal deformation      145
Weak canonical model      107
Weak Hironaka theorem      3 4
Weierstrass preparation theorem      125
Weight      142 143 168
Weight at least      169
Weighted blow up      142 143 167 170
wt, a weight      168
y $Trace_{Y/X}: g_{\ast}\mathcal{O}_X\rightarrow\mathcal{O}_Y$       154
{D}, the fractional part of divisor D      5
{d}, the fractional part of d\in\mathbb{R}$      5

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