836 Index Leray-Hirsch theorem, 599 limit of one-parameter subgroup, 115, 116, 139, 142, 144 line bundle, 253, 255, 348, see also Cartier divisor ample, 268 f -ample, 331 f -very ample, 331 linearized, 680 pullback of, 258 very ample, 268 linear equivalence, see divisor, linear equivalence of linearized line bundle, see line bundle, linearized linearly equivalent divisors, 256 local ˇ Cech complex, 444 local analytic equivalence, 547 local cohomology, 444–447 local data, 160, 253, 257 toric, 181 local duality, 800 local ring, 6, 156 at a point, 6, 9, 94, 99 at a prime divisor, 157 localization, 5, 9 homogeneous, 317 localization theorem, 600, 645 locally principal divisor, 160 locally irreducible, 563 locally trival fiber bundle, 134 log canonical singularities, 557, 783 log del Pezzo surface, 386 index of, 386 log minimal model, 784, 785 log pair, 557 log resolution, 526, 541 logarithmic 1-forms, 359, 360 logarithmic poles, 360 long exact sequence, 444 lower hull, 742 Macaulay2, 275, 407, 445, 641, 799, 800, 806, 807 BGG package, 809 BoijSoederberg package, 809 NormalToricVarieties package, 799, 808, 812 Polyhedra package, 275, 801 toriccodes package, 799 Magma, 799 maximal Cohen-Macaulay (MCM), 416 maximal projective crepant partial desingularization, 529 maximal spectrum, 4 McKay correspondence, 491, 493 McMullen conjecture, 621, 795 minimal generator, 30 minimal model, 764 log, 784, 785 minimal model program, see MMP minimal surface, 764 Minkowski sum, 65, 192, 318, 794 mirror symmetry, 384, 747, 797 mixed volume, 793, 794 MMP, 764, 783 equivariant, 779 log toric, 783, 785 relative, 779 toric, 774, 778 moment map algebraic, 571 symplectic, 571, 574 monomial Brianc ¸on-Skoda theorem, 540 monomial ideal, 540 Mori cone, 293 of a toric variety, 294, 305, 729 Mori fibration, 764 morphism of varieties, 3, 95 projective, see projective morphism proper, see proper morphism moving cone of a toric variety, 733 of a variety, 732 of the secondary fan, 730, 731, 740 multipliciative subset, 9 multiplicity of a simplicial cone, 300, 465, 519, 520 properties of, 519 multiplier ideal, 542, 545 toric, 542, 545 multiplier module, 545 N-Minkowski summand, 283 Nakayama’s Lemma, 169 nef cone, 293 of a toric variety, 294, 728, 730, 733 nef divisor, see Cartier divisor, nef and Q-Cartier divisor, nef Newton polytope, 188, 746, 793 nilpotents, 4, 8, 9, 48, 103, 105 Noether’s theorem, 505, 511, 630 Noetherian, 156 nonassociative product, 746, 747 nonequivariant limit, 599, 601, 625, 644 nonnormal toric variety, 150 nonsingular point, 6 normal affine toric variety, 37 polyhedron, 322 polytope, 68, 86, 372, 805 toric variety, 86, 107 variety, 5, 100 normal bundle, 355, 633, 650, 656 normal fan of a polyhedron, 321, 692, 693
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