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Mumford D., Fogarty J., Kirwan F.C. — Geometric invariant theory
Mumford D., Fogarty J., Kirwan F.C. — Geometric invariant theory



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Название: Geometric invariant theory

Авторы: Mumford D., Fogarty J., Kirwan F.C.

Аннотация:

Just over ten years have passed since the publication of the second edition of this book. In these ten years there have been many developments relating to geometric invariant theory. So many, in fact, that although the new references in this edition outnumber the references in the second edition by a very large margin they form only a selection of the work done in this area in the last decade1. This edition of the book has been extended to take account of one of these developments, one which was just hinted at in the second edition2. A close and very fruitful relationship has been discovered between geometric invariant theory for quasi-projective complex varieties and the moment map in symplectic geometry, and a chapter has been added describing this relationship and some of its applications. In an infinite-dimensional setting the moment map links geometric invariant theory and Yang-Mills theory, which has of course been the focus of much attention among mathematicians over the last fifteen years.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 3-d edition, enlarged

Год издания: 1994

Количество страниц: 305

Добавлена в каталог: 22.12.2013

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Предметный указатель
$Div^{d, d, \ldots, d}[(\check{\mathbf{P}}_{n})^{r+1}]$      109
$D_{\alpha_{0}, \ldots, \alpha_{n}}$      68
$HO(\Phi)$      245
$H_{\nu}$      99
$J^{(d)}$      119
$L^{\Delta}$ of a homomorphism      121
$p(\lambda)$      55
$Pic^{G}$      32
$Pic^{\tau}(X)$      97
$p_{1}$, $p_{2}$ projections      2
$S_{r}(X)$      10
$S_{\beta, m}$, $S_{\beta}$      166 172
$U_{R}$      68
$X^{min}$      153
$X^{reg}$      10
$X^{s}$, $X^{ss}$, $X^{s}_{(i)}$, $X^{s}_{(0)}$      37 194
$\check{\mathbf{P}}_{n}$      109
$\delta(G)$      58
$\Delta_{P}(G)$      60
$\Gamma(T)$, $\Gamma^{Q}(T)$, $\Gamma^{R}(T)$      56
$\kappa(i)$      69
$\Lambda$ of an invertible sheaf      120
$\lambda_{j}$      69
$\mathfrak{K}$, $\ell$      144
$\mathfrak{K}_{\zeta}$      146
$\mathscr{A}$      182
$\mathscr{A}^{(1, 1)}$      183
$\mathscr{A}^{(d)}_{g, 1}$      234
$\mathscr{A}_{g, d, n}$      129 234
$\mathscr{C}$, $\mathscr{C}_{\mu}$      186
$\mathscr{G}$      182
$\mathscr{H}_{g, d, n}$      130
$\mathscr{M}^{'}_{g}$      101
$\mathscr{M}_{g}$      98 228
$\mu(k)$      69
$\mu^{L}(x, \lambda)$      49
$\nu^{L}(x, \delta)$      58
$\psi_{f}$, $\Psi$      3
$\rho(\delta, \epsilon)$      59
$\sigma$ action      2
$\sigma(x)$      7 10
$\tau(x)$      7
$\theta$-polarization      118
$||\lambda||$      58
Abelian scheme      115
Action of a group      2
Action, closed      9
Action, free      10
Action, proper      10
Action, separated      9
Algebraic group      2
Algebraic group, reductive      26
Algebraic pre-scheme      1
Antipodal points in flag complex      61
Binode      80
Cartier divisor, relative      24
Categorical quotient      3
Chow divisor      113
Chow point, chow form      89 109
Classical operations      79
Closed action      9
Coarse moduli problem      97
Coarse moduli scheme      99 129
Codimension two condition      193
Convex set in flag complex      63
Curve over S      98
Cusp      80
Cycle(X)      113
Div of a morphism      107
Div of a sheaf      105
Dual abelian scheme      118
Dual action      25
Equivariant cohomology      165
Etale slice      198
Fine moduli problem      97
Fine moduli scheme      99 129
Flag complex      57
Flag complex, footnote      61
Free action      10
Gauge group      182
Generic stability      200
Geometric quotient      4
Geometric reduction      160
Geometrically reductive      191 201
Grassmannian scheme      86
Group scheme      2
Hamiltonian flow      147
Hamiltonian function      145
Hilbert point      215
Hilbert scheme      21 99
Hyperkaehler quotient      154
Hyperosculation      245
Invariant      25
Jacobian functor      142
k-fold tangent      80
Kaehler quotient      152
Level n structure      129
Line in flag complex      62
Linear rigidification      130
Linearization of invertible sheaf      30
Linearly reductive group      26 191
Marsden — Weinstein reduction      146
Moduli functor, abelian schemes      129
Moduli functor, curves      98
Moduli scheme, abelian schemes      129
Moduli scheme, curves      99
Moment map      145
O(x), O(f) orbit      3
One-parameter subgroup, 1-PS      48
Orbit      3
Partial desingularization      158
Period map      221—223
Picard scheme      22
Poincare series      166
Polarization      97
Polarization of abelian scheme      120
Pre-stable point      36
Principal fibre bundle      16
Projective adjoint action      88
Proper action      10
Properly stable point      37 194
Quantics      76 79
quiver      212
Quotient, categorical      3
Quotient, geometric      4
Quotient, universal      4
R-partition      68
Reduced Poisson algebra      160
Reductive group      26 191 201
Regular point of an action      10
Relative Cartier divisor      24
Representation      24
Reynolds operator      26
S(x), S(f) stabilizer      3
Semi-convex      63
Semi-stable point      36 194
Separated action      9
Stabilizer      3
Stable curve      228
Stable O-cycle in $\mathbf{P}_{n}$      73
Stable point      36 194
Stable vector bundle      224
Strongly etale      198
Submersive      4
Symplectic quotient      146
T, t, $t_{+}$, t*, $t^{*}_{+}$      162 167
Tacnode      80
Torelli's theorem      143
Uniform categorical quotient      4
Uniform geometric quotient      4
Universal categorical quotient      4
Universal geometric quotient      4
Unode      80
Unstable point      194
Variety      1
X//G      148
Yang — Mills equations      182
Yang — Mills functional      182
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