Hertling C. — Frobenius manifolds and moduli spaces for singularities :: Электронная библиотека попечительского совета мехмата МГУ

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Hertling C. — Frobenius manifolds and moduli spaces for singularities

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Название: Frobenius manifolds and moduli spaces for singularities

Автор: Hertling C.

Аннотация:

For those working in singularity theory or other areas of complex geometry, this volume will open the door to the study of Frobenius manifolds. In the first part Hertling explains the theory of manifolds with a multiplication on the tangent bundle. He then presents a simplified explanation of the role of Frobenius manifolds in singularity theory along with all the necessary tools and several applications. Readers will benefit from this careful and sound study of the fundamental structures and results in this exciting branch of mathematics.

Язык:

Рубрика: Математика/Алгебра/Алгебраическая геометрия/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2001

Количество страниц: 270

Добавлена в каталог: 17.03.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

      171 188 191
      168
$H^{\infty}$       110 136 189 196
$\mathcal{H}^{(0)}$       172 174
$\mathcal{H}^{(k)}\subset i_{\ast}\mathcal{H}$       168
$\mu$ -constant family      193
$\mu$ -constant stratum      53 218
$\mu$ -homotopy class      241
$\tau$ -function      252
Analytic spectrum      11 24 56
Automorphism group      52
Bifurcation diagram      36 161
Birkhoff problem      120 214 216
Boundary singularity      69
Brieskorn lattice      114 172 188
Canonical coordinates      18 160
Canonical extension      142
Caustic      13 36 161
Classifying space for Brieskorn lattices      194
Classifying space for PMHSs      188
Cohomology bundle      168
Covariant derivative      20 146
Coxeter group      75 83
Critical space      62
Darboux — Egoroff equations      253
De Rham cohomology      174
Deformed flat coordinates      205
Deligne’s $I^{p,q}$       184
Development      30 41 246
Discriminant      36 40 47 161
Discriminant of a singularity      66 167
Eigenspace      111
Eigenspace decomposition      10
Elementary part      112
Elementary section      110 136
Euler field      14 25 29 146
Exhaustive filtration      117
F-manifold      14
Filtration      114 115 117
First structure connection      154 205
Flat coordinates      147
Flat metric      83
Flat vector bundle      109
Fourier — Laplace transformation      156 214 216
Free divisor      47 134
Frobenius algebra      10
Frobenius manifold      22 83 146
Front      30
G-function      251
Gaub — Manin connection      170
Gaub — Manin system      179 181
Gelfand — Leray form      171
Generalized Milnor fibration      168
Generating family      59 68
Generating function      30 36
Good section      122
Gorenstein ring      10
Gromov — Witten invariants      252
Grothendieck residue      180
Group of symmetries      235
Higher residue pairings      180 191
Hypersurface singularity      62 165
Infinitesimal Torelli type result      226
Intersection form      150 153 181 189
Isolated hypersurface singularity      62 165
Isomonodromic deformations      252
Jacobi algebra      62
Kodaira Spencer map      62 166
Lagrange fibralion      31
Lagrange map      31
Lagrange variety      24
Lattice      113 115
Lefschetz thimble      215
Levi — Civita connection      146
Lie derivative      14 146
Logarithmic differential form      131
Logarithmic pole      118 134 158 162

Logarithmic vector field      47 131
Lyashko — Looijenga map      30 36 55 80
M-tame function      213 217
Massive      24
Massive Frobenius manifold      160
Metric      145
Microdifferential operator      113 174
Milnor fibration      168
Miniversal Lagrange map      33
Mirror Symmetry      211
Mixed Hodge structure      184 193
Modality      53
Moderate growth      112
Moduli of germs of F-manifolds      93
Moduli space $\mathcal{M}_{\mu}$       225 241
monodromy      110 162 189
Monodromy group      153 168 204
Multiplication invariant      10 21 146
Multivalued section      110
Normal crossing case      132 140
Open swallowtail      95
Opposite filtration      122 185 197
Order      112
Oscillating integral      157 214 216
Period map      225
Picard — Lefschetz transformation      153 168
PMHS      184
Poincare rank      134
Polarized mixed Hodge structure      184 192
Polarizing form      184
Pole of order $\leq r+1$       134
Potential      22 147
Potentiality      22 146
Primitive form      104 178 202
Primitive subspace      183 185
Principal part      112
Reduced Kodaira Spencer map      62 163
Reduced Lyashko — Looijenga map      30 39
Reflexive extension      133 139
Regular singular      143
Rellexive      133
Residual connection      135 137 158
Residue endoniorphism      119 135 137 158 162
Restricted bifurcation diagram      38 50 51
Restricted caustic      38
Restricted Lagrange map      34
Riemann — Hilbert problem      120
Riemann — Hilbert — Birkhoff problem      121
Right equivalent      64
Saturated lattice      116 118
Second structure connection      149 204
Semisimple      10
Semiuniversal unfolding      63 165
Simple F-manifold      55 77
Small quantum cohomology      211
Smooth divisor      132
Socle field      249
Spectral number      114 128 193 256
Spectral pair      193
Spectrum of a Frobenius manifold      84 147
Spectrum of a singularity      172
Splitting lemma      67
Stably right equivalent      67
Standard form      43
Strict morphism      185
Symmetries of singularities      235
Torelli type conjecture      225 239
Torelli type result      226
Unfolding      62
Unit field      14
V-filtration      112
Variance      256
Variation operator      189
Versal Lagrange map      33 90
Versal unfolding      63
Virasoro constraints      252
Weight filtration      183

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