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Kollar J. — Rational Curves on Algebraic Varieties
Kollar J. — Rational Curves on Algebraic Varieties



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Название: Rational Curves on Algebraic Varieties

Автор: Kollar J.

Аннотация:

The aim of this book is to provide an introduction to the structure theory of higher dimensional algebraic varieties by studying the geometry of curves, especially rational curves, on varieties. The main applications are in the study of Fano varieties and of related varieties with lots of rational curves on them. This Ergebnisse volume provides the first systematic introduction to this field of study. The book contains a large number of examples and exercises which serve to illustrate the range of the methods and also lead to many open questions of current research.


Язык: en

Рубрика: Математика/Алгебра/Алгебраическая геометрия/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1996

Количество страниц: 320

Добавлена в каталог: 06.05.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$(*\cdot\ldots\cdot*)$      VI.2.6 p.
$(*^*)$      VI.2.6 p.
$*\le_*$, $*<_*$      III.1.1 p.
$*^{sn}$,$*^{wn}$      I.7.2.1 p.
$*^{[-1]}$      I.3.10 p.
$*^{\cap}$      II.4.2.6 p.
$*_*^{-1}( )$      T.3 p.3
$A_*( )$, $AE_*( )$      II.4.1 p.122
$a_*( )$,$a_*( , )$      II.3.12 p.
$B_*( )$, $BE_*( )$      II.4.1 p.122
$Chain_*$( )      IV.4.8 p.212
$Chow^{\mathrm{big}}( )$,$Chow_*^{\mathrm{big}}( )$      1.4.11 p.
$Chow^{\mathrm{small}}( )$, $Chow_*^{\mathrm{small}}( )$      1.4.11 p.
$Ch^{-1}( )$      I.3.24.3 p. I.3.25.2 p.
$Cont_*$      III.1.8 p.
$deg_*( )$      I.3.1 p.41
$deg_{(-K)}( )$      II.3.12 p.
$Hom^{\mathrm{free}}( , )$      II.3.5.4 p.115
$Hom_{bir}( , )$      II.2.6 p.
$Hom_{bir}^n( , )$      II.2.15 p.
$k^{ch}( )$      I.3.24.1 p.
$N_*( )$      II.4.2 p.
$N_*( )$, $NE_*( )$      II.4.1 p.
$RC_*$      IV.4.10 p.
$S^*( )$      I.1.4.1.2 p.
$Univ^{\mathrm{rc}}( )$      II.2.11 p.
$Z_*( )$, $ZE_*( )$      II.4.1 p.
$\equiv$      II.4.1.5 p.
$\mathbb{P}(*,\ldots,*)$      V.1.3 p.
$\mathrm{RatCurves}^n( )$, $\mathrm{RatCurves}^n( , )$      II.2.11 p.
$\rho( )$, $\rho_*$      II.4.6 p.
$\stackrel{a}{\approx}$, $\stackrel{e}{\approx}$, $\stackrel{r}{\approx}$      II.4.1 p.
$\stackrel{e}{\prec}$, $\stackrel{a}{\prec}$      II.4.1.8 p.
$\tilde{*}$      IV.4.2 p.
$\to, \longrightarrow$      T.2 p.3
Algebraic cycle      I.3.1 p.
Algebraic equivalence      II.4.1 p.
Algebraic realization      IV.4.2 p.
Algebraic relation      IV.4.2 p.
Algebraic relation, irreducible      IV.4.2 p.
Algebraic relation, open      IV.4.2 p.
Algebraic relation, proper      IV.4.2 p.
Ample (vector bundle)      II.3.8 p. V.3.9 p.
Anticanonical degree      II.3.12 p.
Anticanonical ring      II.3.3 p.
Attaching trees      II.7.4 p.
Aut( ), $\mathrm{Aut^{\tau}}$      I.1.10.2 p.
Bend-and-break      II.5 p.
Big      T.1 p.3
Birational transform      T.3 p.3
Bundle, $\mathbb{P}^1$-bungle      II.2.5 p.
C Div( )      I.1.12 p.
Canonical ring      III.3.3 p.
Cartier divisor, effective      I.1.11 p.
Cartier divisor, relative      I.1.11 p.
Cayley form      I.3.24.1 p.
CDiv( )      I.1.13 p. II.4.2 p.
ch( )      1.3.24.1 p.
Chain (of smooth rational curves)      II.7.4 p.
Chain, rationally chain connected      IV.3.2 p.
Chow field      I.3.24.1 p.
Chow field condition      I.4.7 p.
Chow form      I.3.24.1 p.
Chow functor      I.3.20 p. I.5.2 p.
Chow pull-back      I.3.18 p.
Chow( )      I.3.21 p.
Chow( ),$Chow_*( )$      I.3.20 p. I.5.3 p.
Closed under *      IV.2.1 p.
Comb      II.7.7 p.
Cone of curves      II.4.7 p.
Cone of effective cycles      II.4.1.7 p.
Connected by a *-chain      IV.4.7 p.
Connected, connected by a *-chain      IV.4.7 p.
Connected, rationally chain connected      IV.3.2 p.
Connected, rationally connected      IV.3.2 p.
Connected, separably rationally connected      IV.3.2 p.
Connected, two general points can be connected by a *-chain      IV.4.9 p.
Contractible      II.5.2 p.
Cycle defined over a subfield      I.3.1.7 p.
Cycle effective      I.3.1 p.
Cycle theoretic fiber      I.3.9 p. I.3.10.4 p.
Cycle, algebraic      I.3.1 p.
Cycle, degree of a cycle      I.3.1.5 p.
Cycle, essentially the same      I.3.8 p.
Cycle, nonnegative      I.3.1 p.
Cyclic cover      II.6.1.5 p.
Deformation, general deformation      II.3.6 p.
Degree (of a cycle)      I.3.1.5 p.
Degree * uniruling      IV.l.l p.
Degree, anticanonical      II.3.12 p.
Del Pezzo surface      III.3.1 p.
DVR      T.5 p.3
E( ), $E^*( )$      I.2.2.2—3 p. I.2.5 p.
Equivalence (algebraic, effective algebraic, effective rational, numerical, rational)      II.4.1—2 pp.
Equivalence relation      IV.4.2 p.
Equivalent (algebraically, rationally, numerically)      II.4.1—2 pp.
Equivalent, set theoretically equivalent      IV.4.2 p.
Essentially independent (family of cycles)      I.3.8 p.
Exceptional set      VI.1.1 p.
Extremal ray      II.4.9 p.
Extremal subcone      II.4.9 p.
Extremal, *-negative extremal ray      II.4.9.4 p.
Fam( )      II.3.12 p. II.4.1.9 p.
Family of algebraic cycles      I.3.10—11 p.
Family of rational curves      II.2.11 p.
Family of rational curves through *      II.2.11 p.
Family, unsplit family of rational curves      IV.2.1 p.
Fano variety      V.l.l p.
Fano variety of lines      V.4.2 p.
Fano variety, $\mathbb{Q}$-fano variety      V.l.l p.
FC      I.6.3 p.
Fiat section      II.5.4 p.
Fiber, cycle theoretic      I.3.9 p. I.3.10.4 p.
Fibration, maximal rationally chain connected      IV.5.1 p.
Fibration, maximal rationally connected      IV.5.3 p.
Fibration, rationally chain connected      IV.5.1 p.
Field of condition      I.4.7 p.
Field of definition      I.1.15 p.
Field, $C_r$-field      IV.6.4.1 p.
Field, Chow field      I.3.24.1 p.
Field, Chow fild condition      I.4.7 p.
Finite type (property)      II.5.10.2 p.144
Flat pull back      I.3.1.4 p.
Form, Cayley      I.3.24.1 p.
Form, Chow      I.3.24.1 p.
Form, normic      IV.6.4.2 p.
Free morphism      II.3.1 p.
Free morphism over *      II.3.1 p.
Free morphism, minimal      IV.2.8 p.
Fundamental cycle      I.3.1.3 p.
General deformation      II.3.6 p.
General point      T.4 p.
General, very general point      T.4 p.3
Generically unobstructed      I.2.11 p.
Geometrically irreducible      II.2.9.1 p.
Geometrically normal      I.6.4.3 p. II.2.9.1 p.
Geometrically rational      II.2.1 p. IV.3.1 p.
Geometrically rational components      II.2.1 p.
Geometrically reduced      I.6.4.3 p.
Geometrically ruled      IV.1.1.4 p.
Geometrically smooth      I.6.4.3 p.
Grass( , )      I.1.7.1 p. I.1.7.2 p.
Grassmann functor      I.1.7.1 p.
Group scheme      I.1.10.2 p.
Handle      II.7.7 p.
Hilb( ),$Hilb_*( )$      I.1.3 p.9 I.1.4 p.10 I.5.2 p.74
Hilbert functor      I.1.3 p. I.5.2 p.
Hilbert polynomial      I.1.2.1 p.
Hom( , )      I.1.9 p. I.1.10 p.
Hom( , , )      II.1.4 p. II.1.4 p.
Horn functor      I.1.9 p.
Incidence correspondence      I.3.23 p.
Index (of a Fano variety)      V.1.9 p.
Inseparably unirational      IV.3.12.1 p.
Inseparably uniruled      VI.3.12.1 p.
Intersection number      VI.2.6 p. VI.2.7.4 p.
Line      V.1.13 p.
Locally unobstructed      I.2.11 p.
Locus      II.2.3 p. III.1.5.1 p.
Locus( )      II.2.3 p. III.1.5.1 p.
MAP      T.2 p.
Maximal rationally chain connected fibration      IV.5.3 p.
Maximal rationally connected fibration      IV.5.1 p.
Minimal (free morphism)      IV.2.8 p.
Modification, ruled      VI.1.6 p.
Modification, uniruled      VI.1.6 p.
Morphism      T.2 p.
MRC-fibration      IV.5.3 p.
MRCC-fibration      IV.5.1 p.
N( ), NE( ),$\overline{NE}( )$      II.4.7 p.
Nef vector bundle      V.3.9 p.
Nef, *-nef      II.4.2.7 p.
Nonnic form      IV.6.4.2 p.
Normal form      IV.4.4.5 p.
Normal point      I.6.4 p.
Normal, geometrically      II.2.9.1 p.
Normal, serni      I.7.2.1 p.
Normal, weakly      I.7.2.1 p.
Numerical equivalence      II.4.2 p.
Obs( )      I.2.6 p.
Obstruction      I.2.2.3 p. I.2.5 p.
Obstruction space      I.2.6 p.
Obtained from * by attaching trees      II.7.4 p.
Picard number      II.4.6 p.
Point, general      T.4 p.
Point, normal      I.6.4 p.
Point, reduced      I.6.4 p.
Point, smooth      I.6.4 p.
Point, very general      T.4 p.3
Prerelation      IV.4.6 p.
Prime divisor (of a field)      VI.1.3.1 p.
Proalgebraic relation      IV.4.2 p.
Product (of algebraic relations)      IV.4.3 p.
Product (of relations)      IV.4.1 p.
Pull-back, Chow pull-back      I.3.18 p.
Pull-back, flat      I.3.1.4 p.
Push forward      I.3.1.2 p. I.6.7 p.
Quot scheme      I.5.15 p.
Quot( , )      I.5.15—16 p.
R( , )      III.3.3 p.
rational      II.2.1 p. IV.3.1 p.
Rational equivalence      II.4.1 p.
Rational, geometrically      II.2.1 p.
Rationally chain connected      IV.3.2 p.
Rationally chain connected fibration      IV.5.1 p.
Rationally connected      IV.3.2 p.
Rationally, maximal rationally chain connected fibration      IV.5.1 p.
Rationally, maximal rationally connected fibration      IV.5.3 p.
Rationally, separably rationally connected      IV.3.2 p.199
RatLocus( )      II.2.3 p.
Ray, *-negative extremal      II.4.9.4 p.
Ray, extremal      II.4.9 p.
Reduced point      I.6.4 p.
Reduced, geometrically      II.2.9.1 p.
Reduction, mod *-reduction      II.5.10.1 p.
Relation      IV.4.1 p.
Relation algebraic      IV.4.2 p.
Relation class      IV.4.2 p. IV.4.6 p.
Relation, equivalence      IV.4.2 p.
Relation, irreducible      IV.4.2 p.
Relation, open      IV.4.2 p.
Relation, proalgebraic      IV.4.2 p.
Relation, proper      IV.4.2 p.
Represent (a functor)      I.1.1 p.
Root, $*^{th}$ root of *      II.6.1.5 p.
Ruled      IV.1.1 p.
Semi normal      I.7.2.1 p.
Semi normalization      I.7.2.1 p.
Semi positive (vector bundle)      II.3.8 p.
Separably rationally connected      IV.3.2 p.
Separably ruled      IV.1.1 p.
Separably uniruled      IV.1.1 p.
Seshadri constant      VI.2.18.6 p.
Smooth point      I.6.4 p.
Smoothable      II.1.10 p. II.7.1 p.
Smoothable fixing *      II.7.2 p.
Smoothing      II.1.10 p. II.7.1 p.
Smoothing, nearby smoothing      II.7.1 p.
Subcomb      II.7.7 p.
Supporting function      II.4.9 p.
Surface, Del Pezzo surface      III.3.1 p.
Tooth      II.7.7 p.
TREE      II.7.4 p.
u( ), $\overline{u}( )$      IV.1.7.3 p.186
Unirationa, separably      IV.3.1 p.
Unirational      IV.3.1 p.
Unirational, inseparably      IV.3.12.3 p.
Uniruled      IV.l.l p.
Uniruled inseparably      IV.3.12 p.
Uniruled separably      IV.l.l p.
Uniruled with curves of *-degree *      IV.1.4 p.
Uniruling, degree * uniruling      IV.l.l p.
Univ( ), $Univ_*( )$      I.1.4 p. I.3.21 p.
Universal element      I.1.1 p.
Universal family      I.1.1 p.9
Unobstructed      I.2.6 p.
Unobstructed generically      I.2.11 p.33
Unobstructed locally      I.2.11 p.33
Unsplit (family of morphisms or rational curves )      IV.2.1 p.
Unsplit, generically unsplit      IV.2.1 p.
Very general point      T.4 p.
WDiv( )      II.4.2 p.
Weak normalization      I.7.2.1 p.
Weakly normal      I.7.2.1 p.
Weighted projective space      V.1.3 p.
Well defined family of algebraic cycles      I.3.10 p. I.3.11 p.
Well formed (weighted projective space)      V.1.3 p.
[]      I.3.1.3 p.
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