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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