832 Index canonical sheaf, 356, 365 of a toric variety, 366 canonical singularities, 549 Caratheodory’s ´ theorem, 69, 537 Cartan matrix, 500 Cartesian diagram, 677 Cartier data, 181, 193, 793 Cartier divisor, 160 ample, 268, 269, 271, 305, 790 basepoint free, 258, 262, 266, 269, 291, 329, 728 big, 427, 658 f -ample, 331, 774 f -very ample, 331 local data of, 160 nef, 291, 305, 728 numerical equivalence of, 292 numerically equivalent to zero, 292 of a polyhedron, 322 of a polytope, 182 on an irreducible variety, 257 torus-invariant, see torus-invariant, Cartier divisor very ample, 268, 269 ˇ Cech cochains, 389 ˇ Cech cohomology, 389–391 ˇ Cech Complex toric, 398 ˇ Cech complex, 389, 390 ceiling , 424 central hyperplane arrangement, 285 chamber, 720, 727 character, 11 generic, 709, 720 Chern character, 625, 627, 631, 633, 811 equivariant, 644 Chern class, 607, 626 of a locally free sheaf, 626 of a smooth variety, 626 of a toric variety, 627 total, 626 Chern roots, 628, 633 of a locally free sheaf, 633 Chevalley’s theorem, 144 Chow group, 613 Chow polytope, 746 Chow ring, 613 of a toric variety, 617, 793 rational, 614 circuits, 703, 753 oriented, 753 class group, 161, 350 classical topology, 4, 50, 102, 113, 139, 142 closed half-space, 25, 63 CoCoA, 799 codimension of a prime ideal, 157 coding theory, 798 Cohen-Macaulay variety, 394 toric, 415, 792 coherent sheaf, 166 cohomology class, 593, 675 equivariant, 601, 608 refined, 593, 675 combinatorially equivalent polytopes, 65 compact, 113, 139, 142 compatibility conditions, 97, 252 compatible map of lattices, 125 complete fan, 113, 139, 142, 193, 790 complete linear system, 261 complete variety, 141, 143 toric, 142 complex, 388 exact sequence of, 388, 389 Koszul, 403, 408 map of, 388 computer algebra 4ti2, see 4ti2 GAP, see GAP Gfan, see Gfan LattE, see LattE Macaulay2, see Macaulay2 Magma, see Magma Normaliz, see Normaliz PALP, see PALP Polymake, see Polymake Sage, see Sage Singular, see Singular TOPCOM, see TOPCOM cone convex polyhedral, see polyhedral cone Gorenstein, 379 of a polyhedron, 319, 325 of a polytope, 24, 70, 86 polyhedral, see polyhedral cone rational polyhedral, see rational polyhedral cone reflexive Gorenstein, 379 simplicial, see simplicial cone smooth, see smooth cone strongly convex, see strongly convex cone connecting homomorphism, 388 conormal sheaf, 355 constant sheaf, 396 constructible set, 123 continued fraction Felix Klein, 476 Hirzebruch-Jung, 468, 469, 473 ordinary, 475, 476 contractible, 396 convergents, 469, 475 convex function, 264 hull, 24 polyhedral cone, see polyhedral cone convex support of full dimension, 265

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