Index absolutely ample, 345 abstract variety, 97, 99 adjunction formula, 366, 503 affine piece of a variety, 51, 52 scheme, 4, 104 toric variety, 12, 18 of a cone, 30 variety, 3 affine cone of a projective toric variety, 56 of a projective variety, 50 affine hyperplane, 63 affine morphism, 397 affine semigroup, 16 Alexander duality, 420, 675 Alexandrov-Fenchel inequality, 794 algebraic action, 12, 106, 199 algebraic cycle, 613 rationally equivalent to zero, 613 algebraic statistics, 798 algebro-geometric imperialism, 796 almost geometric quotient, 201, 202, 210, 684 almost homogeneous variety, 793 ample, see Cartier divisor, ample absolutely, 345 relatively with respect to f , 345 analytic variety, 547 annihilator, 416 arithmetically Cohen-Macaulay (aCM), 415 associahedron, 745, 747, 751, 802 augmentation ideal, 656 β-basis, 736 barycentric subdivision, 525 basepoint free, see also sheaf, generated by global sections Cartier divisor, see Cartier divisor, basepoint free subspace of global sections, 257 basic simplex, 68 Bernoulli numbers, 628, 665 Bertini theorem, 509 Betti numbers, 587, 589, 621 binomial, 16 birational transform of a divisor, 557, 770, 771 Birkhoff polytope, 64 bivariant intersection theory, 677 blowup, 98, 105, 111, 130, 131, 174, 176, 188, 190, 277, 286, 319, 591 of an ideal, 535 Borel construction, 596, 598, 599 for a torus, 596 Borel-Moore homology, 674 Bott formula, 439, 455 branches, 562 Brion’s equalities, 634, 638, 646, 666, 667 for a polytope, 639 bunch of cones, 740 Calabi-Yau variety, 529 cancellative semigroup, 22 canonical bundle, 356 canonical class, 356 canonical divisor, 356, 373 of a toric variety, 366, 793 relative, 541 canonical module of a projective toric variety, 371 of an affine toric variety, 371 of the total coordinate ring, 369 831

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