840 Index support function, 183, 715, 727, 793 integral with respect to a lattice, 183 of a Q-Cartier divisor, 408 of a Cartier divisor, 184, 263 convex, 265, 266, 329, 727 strictly convex, 271, 329–331, 334, 518 of a polytope, 186 support of a divisor, 159 support of a fan, 106, 113, 790 supporting affine hyperplane, 63 supporting half-space, 25 supporting hyperplane, 25 Sylvester sequence, 92 symbolic powers, 545 symmetric algebra, 597 symplectic geometry, 574 symplectic reduction, 575 2-neighborly polytope, 73 tangent bundle, 352 tangent sheaf, 352 tautological bundle, 254, 256, 260 Taylor resolution, 448, 449 tensor product, 8, 48 of sheaves, 249, 255, 350 tent analogy, 264, 267 terminal lemma, 556 terminal singularities, 549, 764 Todd class, 625, 628, 632 equivariant, 644 mock, 655 of a simplicial toric variety, 655 of a smooth toric variety, 629, 811 Todd operators, 666 Todd polynomial, 629 TOPCOM, 799, 802 topological pseudomanifold, 619 torhom, 586 toric Chow lemma, 275 toric cone theorem, 294, 729 toric fibration, 134 toric ideal, 15, 798 toric Kleiman criterion, 291 toric minimal model progam, see MMP, toric toric morphism, 41, 42, 125, 135 projective, 330, 334, 792 proper, 144, 792 toric set, 21 toric singularities canonical, 550–552, 554 finite quotient, 548 klt, 558, 783 log canonical, 558, 783 simplicial, 548 terminal, 551, 554, 555, 776 toric surface resolution of singularities, 465, 470 singular points, 459 smooth classification, 495, 496, 792 toric topology, 574 toric variety, 106 affine, see affine, toric variety complete, see complete variety, toric name, 793, 794 nonnegative points of, 568 normal, see normal, toric variety of a fan, 107 of a polyhedron, 321, 694 of a polytope, 83, 108 positive points of, 568 projective, see projective toric variety quasiprojective, see quasiprojective toric variety quotient construction, see quotient construction semicomplete, 736 semiprojective, see semiprojective toric variety topological model of, 574 toroidal variety, 792 torsion submodule, 444 torsion-free semigroup, 22 torus, 5, 10 embedding, 108, 793, 794 of a projective toric variety, 58 of an affine toric variety, 13 orbit, 118 torus-invariant Cartier divisor, 176 prime divisor, 170 Weil divisor, 172, 175 total coordinate ring, 207, 219, 248, 309, 362, 446, 797 transportation polytope, 64 triangulation, 741, 746, 747, 763 regular, 742, 745, 747 tropical polynomial, 188 tropical variety, 188 tropicalization, 188 twist of a sheaf, 421 unibranch, 563 unimodular polytope, 87 unipolar variety, 767 unique factorization domain (UFD), 7 universal coefficient theorem, 598 universal covering space, 563 universally closed, 143 valuative criterion for properness, 148 Van Kampen theorem, 566 Vandermonde identity, 439, 442 vanishing theorem Batyrev-Borisov, 413, 415, 425 Bott-Steenbrink-Danilov, 421, 423, 793 Demazure, 410, 425, 790, 793 Grauert-Riemenschneider, 428

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