198 INDEX
equivalent rational functions, 133
Eremenko, Alex, 6, 8, 10, 11, 77, 91, 96,
133, 135, 141, 147, 159, 161, 162, 167,
168, 170, 171, 184
Euclid, 8
Euler characteristic, 111
facet inequalities, 81
facial system, 33
fewnomial, 4, 49, 62, 73
dense, 74, 75
Fiedler-Le Touz´ e, everine, 10, 77
flag, 117
isotropic, 173
osculating, 119, 121, 173
secant, 170
flag manifold, 179, 180
flat family, 40
flex, see also point, inflection
Fourier, Joseph, 14
Fulton, William, 105, 113
fundamental cycle, 11, 82
fundamental weights, 152
Gabrielov, Andrei, 6, 8, 10, 11, 77, 91, 96,
133, 135, 141, 147, 159, 161, 162, 167,
168, 170, 171, 184
Gahleitner, Johannes, 10
Gale dual, 64
Gale duality for polynomial systems, 62
Gale transform, 65
Gathmann, Andreas, 9
Gaudin Hamiltonians, 152, 154
Gaudin model, 152
Gaussian elimination, 125
Gessel, Ira, 104
Gr¨ obner basis, 17, 18, 58
Gr¨ obner degeneration, see also toric
degeneration
Grassmannian, 5, 96, 116, 121
Lagrangian, 175
orthogonal, 173
Gromov-Witten invariants, 118
Grothendieck, Alexander, 58
Haas, Bertrand, 4, 54, 75
Harris, Joe, 5, 9, 126, 164
Hasse diagram, 91
Hausdorff distance, 136
Hausdorff metric, 136
Hibi, Takayuki, 95
highest weight module, 153
Hilbert function, 31
Hilbert polynomial, 30
Hilbert, David, 163
Hillar, Chris, 89
Hodge, William Vallance Douglas, 98
homogeneous coordinate ring, 30
homology, 11, 82
hyperboloid of one sheet, 6
hyperplane arrangement, 63
essential, 64, 114
flat of, 70
hyperplane complement, 63
chamber, 70, 114
ideal
initial, 40
order, 91
Pl¨ ucker, 98
radical, 44
toric, 40
initial form, 33, 40
initial scheme, 40
initial system, see also facial system
isotopy, 136
Itenberg, Ilia, 9, 54, 77
utler, Bert, 10
Kharlamov, Viatcheslav, 9, 10, 77, 110
Khovanskii number, 4, 50
Khovanskii, Askold, 3, 4, 13, 19, 26, 29, 49,
50, 54, 75
Klein, Felix, 165
Kontsevich, Maxim, 8
Kostka number, 143
Kushnirenko, Anatoli, 3, 4, 25, 26, 49, 54
Lagarias, Jeff, 54
Lagrange, Joseph Louis, 15
Lagrangian Grassmannian, see also
Grassmannian, Lagrangian
lattice index, 28
Lemma
Schubert, 126, 127
Shape, 17
length of a permutation, 103
Li, Tien-Yien, 4, 54
linear algebraic group, 179
linear projection, 79
Littlewood-Richardson rule, 118, 153
Macdonald, Ian, 112, 113
Manin, Yuri, 8
Markwig, Hannah, 9
master function, 63, 114, 148
Megyesi, Gabor, 113
Mikhalkin, Grisha, 9, 77
Minkowski sum, 3, 27
Minkowski, Hemann, 27
mixed volume, 3, 27
Mukhin, Eugene, 2, 6, 118, 121, 147, 150,
151, 156, 159, 161–164, 166, 171, 174,
175
Nakayama, Hisashi, 78
necklace, 185
net, 136
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