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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