Index 833 coordinate ring, 3, 4 homogeneous, 49, 372 total, see total coordinate ring cotangent bundle, 352 of a toric variety, 452 cotangent sheaf, 352 of a toric variety, 359 Cousin problem, 392 Cox ring, 797 Cremona group, 789 crepant morphism, 553 crepant resolution, 527, 529 cup product, 593 D-flop, 784, 785 Dedekind sums, 655 deformation retract, 396 degree of a divisor on a curve, 287 of a line bundle on a curve, 288 of a projective variety, 657 Dehn-Sommerville equations, 436, 438, 439, 590, 621 depth, 394, 416 derivation, 357 torus-invariant, 364 universal, 357 derived functor, 389, 444, 445 determinantal variety, 13 diagonal map, 102 dimension at a point, 6, 101 dimension of a cone, 24 dimension of a module, 416 dimension of a polytope, 63 dimension of a ring, 156 direct image, 166, 392 higher, 393 left exact, 364 direct limit, 100, 245 directed set, 182, 245 directed system, 245 discrepancy, 549 discrete valuation, 155 discrete valuation ring (DVR), 155 distinguished point, 116, 118, 130, 135 division algorithm, 475 modified, 460, 467 divisor anticanonical, 379 toric, 380 canonical, see canonical divisor Cartier, see Cartier divisor linear equivalence of, 160, 350 locally principal, see locally principal divisor nef, see Cartier divisor, nef numerically effective, see Cartier divisor, nef of a character, 171 of a rational function, 159 of poles, 160 of zeros, 160 principal, 159 Weil, see Weil divisor divisorial wall, 752 double dual, 347, 350 double point, 462 doubly-stochastic matrix, 64 Du Val singularity, 462, 501 dual cone, 24, 801 dual face, 26 dual polytope, 65 dual sheaf, 255, 347, 350 dualizing sheaf, 356 dualizing complex, 395 Dynkin diagram, 462, 467, 500 edge, 25, 63 edge ideal of a graph, 539 effective divisor, 159 Ehrhart polynomial, 432, 508, 657, 793, 807 of a polygon, 433, 434 of a polytopal complex, 434, 442 Ehrhart quasipolynomial, 443 Ehrhart reciprocity, 432, 436, 793 elementary flip, see flip, elementary elementry symmetric polynomial, 628 Enriques-Kodaira classification, 764 equalizer, 95 equivariant cohomology, 596 of a toric variety, 601 equivariant Euler class, 650, 656 equivariant Gysin map, 648, 677, 678 equivariant integral, 645, 678 decomposition of, 649 equivariant map, 41, 126 equivariant Riemann-Roch, 625 for a toric variety, 643 proof of, 650 simplicial, 653, 654 equivariant Todd class, 644 simplicial, 654 equivariant vector bundle, 608 equivariantly formal, 599, 606 Euclidean algorithm, 468, 475 modifed, 468 Euler characteristic decomposition in equivariant case, 645, 647 equivariant, 643 of a sheaf, 430, 440, 625 of a topological space, 442, 505, 586, 627 of a toric variety, 586 Euler class, 626 Euler relation, 365 generalized, 365 Euler sequence, 363, 365

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