Index 2875, lines on a quintic threefold, 77 3264, conics tangent to five conics, 105, 109 affine span, 5, 26, 28 algebraic moment map, 83 algorithm Buchberger, 18 Euclidean, 16, 20, 23 Pieri homotopy, 128 Avenda˜ no, Mart´ ın, 55 ezout, ´ Etienne, 3 Basu, Saugata, 2 Benedetti, Riccardo, 50 Bernstein, Daniel, 3, 4, 25, 26, 34, 49 Bertini, Eugenio, 29 Bertrand, Benoˆ ıt, 56 Bethe Ansatz, 152 Bethe Ansatz equations, 149 Bethe vector, 156 Bihan, Fr´ ed´ eric, 5, 56, 58 bound ezout, 3 Bihan, 56 BKK, 3 Descartes, 13, 49 fewnomial, 4, 5, 49 Khovanskii, 53 lower, 77, 172 polyhedral, 25 upper, 178 Buchberger, Bruno, 18 Budan de Boislaurent, Fran¸ cois, 14 Burda, Yuri, 13, 19 Caporaso, Lucia, 9 Castelnuovo, Guido, 164 Catalan number, 136 Cauchy-Binet formula, 123 chain in a poset, 93 maximal, 93 Chasles, Michel, 105 circuit, 56 near, 75 primitive, 56 Conjecture Bethe Ansatz, 155 Discriminant, 163, 184 Discriminant for Lagrangian Grassmannian, 177 Kushnirenko, 54 Monotone, 180, 184 Monotone Secant, 186 Secant, 170, 171 Shapiro, 6–8, 118, 119, 121, 123, 124, 133, 147, 159, 162, 167, 170, 180, 184 Shapiro for Lagrangian Grassmannian, 177 continued fraction, 19 convex combination, 26 convex hull, 26 coordinates homogeneous, 27 Pl¨ ucker, 96, 123, 126 Stiefel, 96 cover in a poset, 91 critical point, 8, 114, 133 curve convex, 164 maximally inflected, 164 moment, 6 rational, 164 rational normal, 118, 121 rational normal cubic, 79 rational plane cubic, 9 degree mapping, 11, 19–21, 80 of a subvariety, 29 of a zero-dimensional ideal, 17 real, 84 Descartes’s rule of signs, 4, 13, 14 Descartes, Ren´ e, 4, 13 descent of a permutation, 183 Dickenstein, Alicia, 54 Dietmaier, P., 110 discriminant, 26, 162 distributive lattice, 95 echelon form, 125 Ehrhart, Eug` ene, 31 Eisenbud, David, 5, 126, 164 eliminant, 17, 58 enumerative geometry, 105 197
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