838 Index pullback of a torus-invariant Cartier divisor, 281 Q-Cartier divisor, 180 nef, 409 Q-divisor, 424 Q-factorial, 46 Q-Fano variety, see variety, Q-Fano quadratic reciprocity, 794 quasicoherent sheaf, 166 quasicompact, 104 quasiprojective toric variety, 330 quasiprojective variety, 313, 315 quotient almost geometric, see almost geometric quotient geometric, see geometric quotient good categorical, see good categorical quotient quotient construction general toric variety, 216, 217 no torus factors, 210 Q-Weil divisor, 424 round down of, 424 round up of, 424 rank of a coherent sheaf, 348 of a finitely generated abelian group, 524 of a module, 366 rational double point, 462, 464, 467, 500 rational function, 51, 100 rational normal cone, 13, 32, 38, 40, 46, 50, 178, 461, 463 rational normal curve, 50, 57 rational normal scroll, 84, 112 rational polyhedral cone, 29 rational singularities, 546 toric, 546 rationally smooth, 546, 592 ray generator, 29 R-divisor, 424 real projective plane, 72 real torus, 561, 570 recession cone, 318 reduced cohomology, 397 reductive group, 201 Rees algebra, 534 refined cohomology class, see cohomology class, refined refinement of a fan, 130, 373 reflexive polygon, 382, 510 reflexive polytope, 82, 87, 380, 381, 529, 797 classification, 384 reflexive sheaf, 168, 347 of rank 1, 348 regular cone, see smooth cone regular fan, 113 regular local ring, 7, 157 regular map, 93, 98 regular representation, 491 regular sequence, 394 relative case, 729, 735 relative cohomology, 405 relative interior, 27 relatively ample with respect to f , 345 representation ring, 656 representations of finite groups, 491 special, 492 resolution of singularities, 463, 513 crepant, 511, 527 embedded, 530 Grobner ¨ fan, 490 Hironaka, 513 log, 526 minimal, 499 projective, 513 SNC, 526 toric, 520 toric surface, 465, 470 restriction of a divisor, 160 restriction of a sheaf, 166 Riemann-Roch, see also Hirzebruch-Riemann-Roch curves, 503, 630 surfaces, 504, 630 topological part, 505, 630 ring of invariants, 45 ringed space, 95, 99 rooted binary tree, 746, 747 Sage, 522, 631, 641, 799 PALP package, 799 Polyhedra package, 799 TOPCOM package, 802 ToricVarieties package, 799, 810, 811 saturated affine semigroup, 37 secondary fan, 714, 719, 727, 743, 746, 797 chamber of, see chamber moving cone of, see moving cone, of the secondary fan properties of, 720 secondary polyhedron, 746 secondary polytope, 743, 745, 746, 751, 802 section of a sheaf, 165 of a vector bundle, 251 sectional genus, 509, 796 of a toric surface, 509 Segre embedding, 52 self-intersection, 303 semi-stable reduction, 792 semicomplete toric variety, 736 semigroup, 16 semigroup algebra, 16 of a cone, 30 of a polyhedron, 322, 693

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