834 Index generalized, 364 toric, 363 Euler-Maclaurin formula, 665, 669 ´ eventail, 789 exact sequence long, 389 of complexes, 388 of sheaves, 248 exceptional curve of the first kind, 498 exceptional divisor, 464 exceptional locus, 521, 764 exceptional set, 207 of a character, 700 expected dimension, 685, 706, 712, 722 Ext, 395, 445 exterior product, see wedge product extremal wall, see wall, extremal extremal contraction, 764, 765 divisorial, 766, 768, 776, 778 fibering, 766, 768, 778 flipping, 766, 768, 772, 775, 776, 778 structure of, 766, 768 extremal ray, 295, 306, 729, 764, 772 D-negative, 774, 779 extremal walls, 295 f -ample, see Cartier divisor, f -ample f -very ample, see Cartier divisor, f -very ample 4ti2, 72, 799 f.r.p.p decomposition, 791 face, 25, 63 face numbers, 435, 621, 795 facet, 25, 63 normal, 26, 64 presentation, 67 virtual, 698, 699 fake weighted projective spaces, 767 fan, 77, 106, 789, 791 complete, see complete fan degenerate, 278, 692, 721, 722, 751, 768, 779 generalized, 278, 692, 693, 714, 721, 727, 728 infinite, 792 nondegenerate, 278 normal, see normal fan refinement of, see refinement of a fan simplicial, see simplicial fan smooth, see smooth fan Fano type, 559 toric, 559 Fano variety, see variety, Fano fiber bundle, 133 fiber product of varieties, 102 Fibonacci number, 22 finite quotient singularities, 113, 547 finitely generated semigroup, 16 fixed component, 732 fixed points, 598, 647 flip, 750, 763, 764 elementary, 762, 772 Proj construction, 775, 776 termination of, 779–781, 783 toric, 772 flipping wall, 752, 759 floor , 424 flop, 784, 785 formal power series, 10 formal semigroup module, 634 summable elements of, 635 fractional ideal, 170 sheaf of, 540, 792 full dimensional convex support, 265 polyhedron, 319 polytope, 64 function field, 100 functor, 388 derived, 389 fundamental class, 675 fundamental group of a toric variety, 566, 793 of a torus, 562 of an affine toric variety, 565 G-Hilbert scheme, 493, 495 (G,χ)-invariant polynomial, 680, 681 GAGA, 142, 144 Gale duality, 452, 701–703, 713, 736, 743 GAP, 799 toric package, 799 gauged linear sigma model, 797 generalized Euler sequence, 626 generalized Gysin map, 632, 674–676, see also equivariant Gysin map generated by global sections, see sheaf, generated by global sections geometric case, 731, 746, 750, 751 primtive, 733 geometric invariant theory, see GIT geometric modeling, 798 geometric quotient, 200, 202, 210, 684 almost, see almost geometric quotient Gfan, 488, 799, 804 GIT, 679, 680, see also expected dimension general quotient, 686, 701 quotient, 684, 694, 727 GKZ cone, 715–719, 727, 730 facet of, 751 irrelevant ideal of, 722 GKZ decomposition, 720 global sections, 189 of a sheaf, 166, 248 of a toric sheaf, 190, 193 of a vector bundle, 251 gluing data, 97, 252
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