Index 837 of a polytope, 76, 77, 108, 279, 692, 794 normal ring, 5, 156, 157 normal sheaf, 355, 366 Normaliz, 33, 39, 72, 434, 799, 805–807 normalization, 5, 151 of a projective toric variety, 153 of an affine toric variety, 39, 152 of an irreducible curve, 288 normalized basis, 460 normalized volume, 433, 657 Nullstellensatz, 3 numerically effective divisor, see Cartier divisor, nef and Q-Cartier divisor, nef numerically equivalent divisors, see Cartier divisor, numerical equivalence of proper 1-cycles, see proper 1-cycle, numerical equivalence of to zero, see Cartier divisor, numerically equivalent to zero and proper 1-cycle, numerically equivalent to zero one-parameter subgroup, 11 orbifold, 46, 113, 547 orbit closure, 121, 135 Orbit-Cone Correspondence, 119, 791 nonnormal case, 154 order of vanishing, 158 orientation coefficient, 580 oriented circuit, see circuits, oriented oriented matroids, 703 p-allowable, 619 pair (X,D), 557, 783 PALP, 799 parameters of a cone, 460 partial quotients, 469, 475 p-Ehrhart polynomial, 435, 512 perfect field, 48 permutation matrix, 55 perversity, 619 complementary, 619 maximal, 619 middle, 619 minimal, 619 Picard group, 161, 256, 350 of a toric variety, 176, 577 Pick’s formula, 434 piecewise polynomial functions, 606, 607 Poincar´ duality, 593, 620, 675 Poincar´ polynomial, 592 Poincar´ residue, 360, 361 pointed affine semigroup, 36 polar polytope, 65 pole, 159 polyhedral cone, 23 polyhedron, 190, 318 augmented, 713 full dimensional, see full dimensional, polyhedron lattice, see lattice polyhedron normal, see normal, polyhedron of a character, 689, 690 of a torus-invariant divisor, 190, 266, 328 very ample, see very ample, polyhedron Polymake, 799 polynomial splines, 607 polytopal complex, 434 polytope, 24, 63 combinatorially equivalent, see combinatorially equivalent polytopes full dimensional, see full dimensional, polytope lattice, see lattice polytope normal, see normal, polytope simple, see simple polytope simplicial, see simplicial polytope smooth, see smooth polytope unimodular, see unimodular polytope very ample, see very ample, polytope presheaf, 165, 247 prevariety, 102 primary decomposition, 161 prime divisor, 157 primitive collection, 304, 340, 774 primitive relation, 305, 340, 774 principal A-determinant, 746 principal divisor, see divisor, principal principal ideal domain (PID), 156, 157 principalization, 541 product variety, 7, 53, 101, 313 class group of, 175 toric, 47, 90, 111 Proj, 317, 322, 372, 684, 692, 693 projective bundle of a coherent sheaf, 318 of a locally free sheaf, 316 of a vector bundle, 316 toric, 337, 338 projective morphism, 314, 315, 346 projective space, 49 projective toric variety, 55 projective variety, 49 projective with respect to a line bundle, 314, 345 projectively normal variety, 61, 86, 441, 800 proper 1-cycle, 292 numerical equivalence of, 292 numerically equivalent to zero, 292 proper continuous map, 142, 144 proper face, 25 proper morphism, 143, 144, 315 pseudoeffective cone, 732 of a toric variety, 733 Puiseux series, 188 pullback, see line bundle, pullback of

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