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Classical Algebraic Geometry: a Modern View Igor V Cambridge University Press 978-1-107-01765-8 - Classical Algebraic Geometry: A Modern View Igor V. Dolgachev Index More information Symbol index (123, 94), 118 V22, 264 (166), 522 W(EN ), 334 , r (l r), 152 Wg−1, 199 ∨ (a0,...,ar), 511 X , 29 k 2 , 402 X0(n), 85 A f , 36 Δ, 533 Ak, 34 Δk, 533 Bg, 193 Γ(3), 121 C(d), 212 Γ(ϑ), 218 CN , 361 Γ∗(F ), 164 D( f ), 563 ΓT , 212 Dψ, 2 Γ f , 285 φ Dr( ), 162 Λp, 515 ∨ E , 1 Ω(A0), 511 Eg, 193 Ω(A0, A1,...,Ar), 511 F(C), 537 Θ, 199 , G(3 AP3( f ))σ, 263 Θk(A, B), 98 Pn Gr( ), 21 δx, 171 G168, 273 γk, 516 G216, 121 D( f ), 563 HA f (t), 50 Gk, 514 I1,N , 331 P(1, 2, 2, 3, 3), 111 IZ , 38 P(E), 320 KX, 75 V(E), 320 Ln(q), 269 EN , 334 Nθ, 244 Fn, 322 Ω f , 51 kN , 332 H Pak (X), 5 2, 522 Q(V)±, 204 H3(3), 493 [n] Qg, 195 L , 166 Mar RC , 252 3 , 250 ϑ Mev R , 216 3 , 250 Mev Rg, 239 g , 197 S (C), 533 TCd, 197 d S (E), 1 TCX/S , 196 S d(E), 1 A6, 102 S a,n, 347 C, 252, 517 S a1,...,ak,n, 560 C(C), 252 620 © in this web service Cambridge University Press www.cambridge.org Cambridge University Press 978-1-107-01765-8 - Classical Algebraic Geometry: A Modern View Igor V. Dolgachev Index More information Symbol index 621 CW , 528 dom( f ), 280 Cω, 518 pd, 165 a, 202 cx, 171 A : B, 269 BlX(Z), 282 adj(A), 7 k BlX(a), 282 ap , 48 + f BlX(Z), 282 AP( f ), 36 CR4, 478 Nϑ, 245 B.A, 269 S, 119 Bs(| V |), 281 S3, 472 b(| V |), 281 SW , 528 Sω, 518 Catk(d, n), 48 T, 119 Catk( f ), 50 ZX, 517 Cay(| L |), 24 ZG, 510 Cay(X), 21 μn, 245 σm(C), 570 D2(n), 15 τij, 198 Dd(n), 19, 23 Matm,k, 160 ∂ j, 2 Matm,k(r), 161 D(A; u, v), 154 , O(1 N), 331 D(L), 23 Prym(S˜ /S ), 238 Δi ,...,i , 97 SL(2, F ), 121 1 k q Dm,n, 65 Symm(r), 181 f, s o VSP( ) , 47 E, 1 ϑ T , 194 e(X, x), 34 ϑi, jkl, 246 ECa(X), 9 ak, 176 d(ϑ), 218 He(X), 17 d , 176 k He( f ), 4 eγ(z), 200 He( f ), 13 e , 176 k He(X), 13 f , 280 d Hilbs(P(E)), 39 g1, 85 n H (E), 57 i , 529 q W HS(X), 19 iω, 519 k + , 571 m 1 i, 2 pi1...im , 509 qϑ, 188 j, 115 rα, 334 Jac(L), 23 rm, 570 t , 206 g , (n, d, k, s), 45 , 526 [n], 591 L(Z), 54 Λ Arf(q), 191 , 45 Cr(n), 342 Jac(X), 114 μ(φ), 33 Kum(A), 538 multxX, 35 OG(2, Q), 552 μ(X, x), 33 O(N), 334 Pf(A), 108 N( f ), 25 SO(n + 1), 553 Sp(V), 191 Ω f , 51 Ω∨ Tr(A), 97 f , 51 © in this web service Cambridge University Press www.cambridge.org Cambridge University Press 978-1-107-01765-8 - Classical Algebraic Geometry: A Modern View Igor V. Dolgachev Index More information 622 Symbol index O(E, q), 57 st, 20 St(| L |), 23 Pn, 4 P(E), 4 T, 44 PB(| L |), 25 T(E), 1 T Pn, 84, 85 x(X), 7 PO(3), 73 Tφ, 44 PO(n + 1), 63 Tφ, 44 PS(s, d; n), 47 TCa(X), 8 Θk, 97 Ram(φ), 29 U, 235 S 1, S 2 , 559 Vn Sd, 1 d, 32 S (3), 120 vd, 32 S (E), 1 s(n, d), 43 wrk( f ), 52 ΣPGL(E), 11 SL(U), 3 X(3), 117 Sn,C , 86 St(X), 19 Z(s), 87 © in this web service Cambridge University Press www.cambridge.org Cambridge University Press 978-1-107-01765-8 - Classical Algebraic Geometry: A Modern View Igor V. Dolgachev Index More information Subject index (−1)-curve, 248 anti-polar, 51 (−n)-curve, 289 conic, 277 (166)-configuration, 522 anticanonical Ak-singularity, 34 divisor, 387 F-locus, 281 embedding, 264 N-lateral, 256 linear system, 387 α-plane, 512 model β-plane, 512 of a del Pezzo surface, 384 EN -lattice, 361 ring, 385 k-secant line, 215 Antonelli, G., 591 s-lateral, 38 apolar homogeneous form, 35 Abel–Jacobi Theorem, 198 quadrics, 98 abelian surfaces ring, 36 moduli, 545 subscheme, 36 abelian variety apolarity principally polarized, 199 duality, 131 Abo, H., 45 First Main Theorem, 42 absolute invariant, 115 map, 48 aCM of conics, 112 sheaf, 164, 166, 167, 177, 296, 385 Apollonius of Perga, 104 -symmetric sheaf, 168 Apollonius problem, 104 of rank 1, 179 apparent boundary, 7 symmetric, 168 Arbarello, E., xi, 188, 218, 222, 224 subscheme, 296, 297, 299 Arf invariant, 191 ADE singularity, 376 Aronhold invariant, 115, 119, 130 adjoint symbolic expression, 137 orbit Aronhold set, 249 minimal, 553 Aronhold, S., 144, 278 nilpotent, 553 arrangement of lines, 256 supminimal, 553 Artebani, M., 144, 266 variety, 553 Artin, M., 351, 424 adjugate matrix, 7 associated Alberich-Carraminana,˜ M., 334 curve, 570 Alexander, J. E., 42 line, 589 Alexander, J.W., 345 sets of points, 455 Allcock, D., 482 association involution, 478 almost general position, 357 August, F., 451, 452, 505 Altman, A., 170 azygetic, 207 623 © in this web service Cambridge University Press www.cambridge.org Cambridge University Press 978-1-107-01765-8 - Classical Algebraic Geometry: A Modern View Igor V. Dolgachev Index More information 624 Subject index set of seven bitangents, 228 Bos, H., 112 triad of Steiner complexes, 208 Bottema, O., 584 set in a symplectic space, 204 Bourbaki, N., 365, 425, 506, 591 tetrad of bitangents, 229 bracket-function, 467 triad in a symplectic space, 204 Bragadin, G., xii triad of bitangents, 228, 229 Brambilla, M., 42, 45 branch divisor, 29 Bohning,¨ C., 227 Brianchon’s Theorem, 80 Babbage’s conjecture, 184 Brianchon, Ch., 80 Babbage, D.W., 184, 392 Briancon, J., 131 Baker, H., 111, 215, 225, 405, 422, 425, 440, Brill, A., 214, 225 503, 504 Bring curve, 498, 500 Bardelli, F., 250 Brioschi covariant, 140 Barth’s condition, 46 Brioschi, F., 140 Barth, W., 46, 85, 90, 112, 279, 324 Bronowski, J., 67 Bateman, H., 277, 279, 313 Bruno, A., 296 Battaglini line complex, 547, 588 bubble cycle, 308 Battaglini, G., 590 admissible order, 308 Bauer, Th., 85, 90, 112 fundamental, 308 Beauville, A., 168, 185, 186, 197, 392, 553 bubble space, 307 Beklemishev, N., 479 height function, 307 Beltrametti, M., xii proper points, 307 Bertini Burch, L., 453 involution, 317, 413 Burhardt quartic threefold, 186 Theorem Burns, D., 500 on elliptic pencils, 344, 346 on irreducibility, 75, 305, 443 C. van Oss, 276 on singularities, 20, 177, 299, 305, 382, 562 Calabi–Yau variety, 25, 528 Bertini, E., 345, 346, 424 Campbell, J.E., 67 bezoutiant, 184 canonical bielliptic curve, 241 class bifid map, 193 of a Fano variety, 534 binary form of a normal surface, 178 quadratic invariant, 138 of a projective bundle, 321 Binet, J., 591 of a ruled surface, 322, 561 binode, 424 of blow-up, 332 birational map, 280 of Grassmann variety, 75 Birkenhake, Ch., 216 equation biscribed triangle, 244 of plane cubic, 117 of the Klein curve, 274 map, 221 bitangent Caporali quartic, 277 defined by Aronhold set, 228 Caporali, E., 277 honest, 35 Caporaso, L., 204, 228 hyperplane, 204 Carletti, E., xii matrix, 277 Carlini, E., 45 their number, 215 Cartan cubic, 435 bitangential curve, 215, 225 Cartan matrix, 362 Blache, R., 178 irreducible, 363 blowing down structure, 355 Cartan, E., 435 Bobillier, E., 66, 112 Carter, R., 483 bordered determinant, 99, 140, 154, 278 Casnati, G., 168 Bordiga scroll, 300 Castelnuovo, G., 345, 591 Bordiga surface, 300, 423, 440 Castelnuovo–Richmond quartic, 478, 481, 524, Bordiga, G., 300, 423, 440 545 Borel, A., 366 catalecticant, 266 © in this web service Cambridge University Press www.cambridge.org Cambridge University Press 978-1-107-01765-8 - Classical Algebraic Geometry: A Modern View Igor V. Dolgachev Index More information Subject index 625 determinant, 50 Clebsch, A., 138, 140, 142, 144, 278, 424, 479, hypersurface, 50 505 matrix, 48 Clemens, C.H., 224 Catanese, F., 168, 177, 183, 186, 187, 238, 239 Clifford, W., 345 Cayley Coble, A., 112, 211, 224, 251, 278, 425, 481, cubic surface, 449 482, 506, 513 dianode surface, 250 Cohen, T., 266 family of cubic surfaces, 504 Cohen–Macaulay octad, 245 module, 164 quartic symmetroid, 28 sheaf, 169 Cayley, A., 17, 28, 29, 35, 36, 83, 100, 112, 140, variety, 161 141, 144, 181, 214, 225, 250, 278, 345, collineation, 10 433, 504, 549, 590, 591 Colombo, E., 482 Cayley–Brill formula, 214 complete Cayley–Salmon equation, 503 ideal, 283 Cayley–Zeuthen formulas, 564 pentalateral, 256 Cayleyan quadrangle, 264 contravariant, 140 complex equation curve, 21, 65, 142 of a quadric, 99 of plane cubic, 127 complex reflection, 122 variety, 21 group, 103, 122, 276 of a linear system, 24 compound matrix, 98 center variety, 528 adjugate, 98 Chandler, K., 42 conductor formula, 171 characteristic matrix, 330 conductor ideal, 170 Chasles Cone Theorem, 371 covariant quadric, 94, 112 congruence of lines, 513 Principle of Correspondence, 225 class, 513 Theorem order, 513 on conjugate triangles, 77 conic on linear line complex, 525, 590 apolar, 112 on polar tetrahedra, 93 conjugate triangles of, 76 Chasles, M., 93, 111, 112, 144, 224, 590–592 invariants of a pair, 100 Chipalkatti, J., 45 mutually apolar, 103 Chisini, O., 65, 66 Poncelet n-related, 82 Chow Poncelet related, 81 form, 517, 548, 568, 590 self-polar triangles of, 73 group, 290 variety of pairs, 85 ring, 512 conic bundle, 328 Ciani, E., 276, 279 conjugate Ciliberto, C., 14, 67, 393 conics, 112 circle linear forms, 51 complex, 89 linear subspaces, 92 real, 91 triangle, 76 circulant matrix, 48 contact class, 4, 30 curves, 155 of a space curve, 570, 573 conics, 240 of immersion, 564 cubics, 244 Clebsch of degree d − 1, 240 diagonal cubic surface, 439, 497 hyperplane quartic curve, 255 of a canonical curve, 189 nondegenerate, 256 manifold, 553 weakly nondegenerate, 256 contravariant, 22, 136 Theorem, 334 Cayleyan, 140 transfer principle, 138, 474, 481 Hermite, 141 © in this web service Cambridge University Press www.cambridge.org Cambridge University Press 978-1-107-01765-8 - Classical Algebraic Geometry: A Modern View Igor V.
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