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Friedman.R. — Algebraic Surfaces and Holomorphic Vector Bundles
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Название: Algebraic Surfaces and Holomorphic Vector BundlesАвтор: Friedman.R. Аннотация: This book covers the theory of algebraic surfaces and holomorphic vector bundles in an integrated manner. It is aimed at graduate students who have had a thorough first-year course in algebraic geometry (at the level of Hartshorne's Algebraic Geometry), as well as more advanced graduate students and researchers in the areas of algebraic geometry, gauge theory, or 4-manifold topology. Many of the results on vector bundles should also be of interest to physicists studying string theory. A novel feature of the book is its integrated approach to algebraic surface theory and the study of vector bundle theory on both curves and surfaces. While the two subjects remain separate through the first few chapters, and are studied in alternate chapters, they become much more tightly interconnected as the book progresses. Thus vector bundles over curves are studied to understand ruled surfaces, and then reappear in the proof of Bogomolov's inequality for stable bundles, which is itself applied to study canonical embeddings of surfaces via Reider's method. Similarly, ruled and elliptic surfaces are discussed in detail, and then the geometry of vector bundles over such surfaces is analyzed. Many of the results on vector bundles appear for the first time in book form, suitable for graduate students. The book also has a strong emphasis on examples, both of surfaces and vector bundles. There are over 100 exercises which form an integral part of the text.
Язык: Рубрика: Математика /Алгебра /Алгебраическая геометрия /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 1998Количество страниц: 264Добавлена в каталог: 12.03.2005Операции: Положить на полку |
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81 81 205 59 Abelian surface see Surface abelian Abundance theorem 279 293 306 Ad V 99 Adjoint bundle see Ad V Adjunction formula 13 Albanese map 118 289 Albanese variety 288 Algebraic function field 271 275 Allowable elementary modification see Elementary modification allowable Almost decomposable 2 Ample cone 19 Andreotti, A. 278 Anti-serf-dual connection see Connection anti-serf-dual Arithmetic genus see Genus arithmetic Artin's criterion 75 80 Atiyah — Singer index theorem 207 Atiyah's theorem on vector bundles 1 33 Atiyah, M. 1 Auslander — Buchsbaum dimension formula 51 199 Barlow surface see Surface Barlow Barth, W. 3 162 310 Base point, assigned 69 Base point, infinitely near 69 Base point, simple 69 Base point, unassigned 69 Basic elliptic surface see Surface elliptic basic Bauer, S. 240 Big divisor see Divisor big Bloch, S. 312 Blowing down 66 Blowing up 59 Bogomolov number 274 Bogomolov — Miyaok — Yau inequality 1 282 Bogomolov's inequality 3 22 107 149 163 245—247 305 Bogomolov, F. 3 245 Bombieri's theorem 79 248 Bombieri, E. 1 248 Botany 282 Brosius, J.E. 3 150 310 Brussee, R. 312 Canonical bundle formula 176 Canonical curve 134 139 Castelnuovo — deFranchis theorem 283 302 Castelnuovo's criterion 1 64—67 Castelnuovo's theorem 278 Catanese, F. 14 Cayley — Bacharach property 40 126 Chambers of type (w,p) 100 Chern class 27—30 Chern class, total 28 Chevalley, C. 275 Chow group 28 312 Chow's theorem 7 Class field theory 271 Class of type (w,p) 100 Classification of threefolds 305 Clifford's theorem 163 256 Coarse moduli space see Moduli space coarse Compatible pair 186 Complex torus see torus Computation sequence 80 168 Computation sequence, numerically 24 191 Connection 101 Connection matrix 102 Connection, anti-self-dual 105 206 Connection, flat 102 Connection, Hermitian 102 Connection, Hermitian — Einstein 3 104 245 Connection, integrable 102 Connection, irreducible 102 Connection, self-dual 105 Connection, unitary 102 Contraction 66 Cremona transformation 69 Cubic surface see Surface cubic Curvature 102 Cusp 14 23 138 173 Deformation theory 155 Degree of a torsion free sheaf 198 Degree, normalized 85 Del Pezzo surface see Surface del Depth 51 Desale, U.V. 2 Descent theory 145 265 Destabilizing 86 Div X 9 Divisor 9 Divisor class 10 Divisor, big 20 72 Divisor, effective 9 Divisor, nef 20 72 Dolgachev surface see surface Dolgachev Dolgachev, I. 189 278 Donaldson invariant 101 197 203 205 Donaldson polynomial 205 Donaldson polynomial on 206 Donaldson — Uhlenbeck — Yau theorem 106 245 Donaldson, S. 3 208 308 Double cover 2 46—50 57 Double point, ordinary 14 23 133 138 173 241 Double point, ordinary, threefold 210 242 Double point, rational 77—78 81—83 128 129 134 138 178 182 Dual complex 75 Dual graph 75 173 Dualizing sheaf 13 Dynkin diagram 173 Effective see Divisor effective Eimination of indeterminacy 68 Elementary modification 41—42 55 Elementary modification, allowable 148 Elementary transformation 114 118 Elliptic normal curve 128 Elliptic surface see Surface elliptic Embedded resolution 63 Enriques surface see Surface Eariques Enriques' theorem 1 280 Enriques, F. 278 Enumerative geometry 2 3 Enumerative geometry, linear 10 Enumerative geometry, numerical 17 Enumerative geometry, of families of vector bundles 153 Euler characteristic 9 Euler characteristic, holomorphic 9 Euler exact sequence 109 Eventually base point free 21 72 Exceptional curve 66—67 Exceptional divisor 59 Expected dimension 158 Extended root system 173 Extremal rays 305 Factorization of birational morphisms 67 Faithfully flat 275 Fernandez del Busto, G. 245 Fibration 167 Fine moduli space see Moduli space fine Fintushel, R. 240 Flat connection see Connection flat Formal functions theorem 62 65 74 Freedman, M. 278 Fulton, W. 4 28 Fundamental cycle 79—82 191 Galois cohomology 184 185 Galois morphism 272 General type 277; see Surface general Generic rank 26 Genus drop 14 Genus drop, local 14 Genus, arithmetic 13 Genus, geometric 8 Geography 282 Geometric genus see Genus geometric Geometric invariant theory 1 154 Gieseker compactification 206 Gieseker stability see Stability Gieseker Gieseker, D. 2 154 245 257 259 307 310 Godeaux surface see surface Godeaux Gomez, T. 311 Gomprecht, D. 313 Good generic surface see Surface good Good vector bundle see Vector bundle good Grauert's contraction theorem 72 Grauert, H. 72 Griffiths, P. 4 Grothendieck — Riemann — Roch theorem 4 29 48 212 213 215 Grothendieck's theorem on vector bundles 1 33 Grothendieck, A. 1 154 GSttsche, L. 206 Harder — Narasimhan filtration 97 112 Harris, J. 4 Hartogs' theorem 60 67 Hartshorne, R. 3 259 Hermitian — Einstein connection see Connection Hermitian Hilbert scheme 155 164 204 Hirzebruch signature theorem 9 22 Hodge index theorem 9 16—18 23 Hodge theory 8—9 17 Homological invariant 186 Hoppe, H.-J. 3 310 Horikawa surface see Surface Horikawa Horikawa, E. 282 Hulek, K. 3 162 310 Hyperelliptic surface see Surface hyperelliptic Infinitely near 63 Intersection pairing 8 11 Irregularity 8 Irregularity, birational invariance of 62 70 Italian algebraic geometry 1 278 J-function 185 Jacobinn elliptic surface see Surface elliptic Jacobian Jordan — Hoeder filtration 112 154 K3 surface see Surface K3 Kaehler identities 105 106 Kaeler manifold 101 103 Kametani, Y. 218 Kawamata — Viehweg vanishing theorem 245 Klein, F. 63 Kobayashi — Hitchin conjecture 3 Kobayashi, S. 3 106 Kodaira classification 7 Kodaira classification of surfaces 278 Kodaira dimension 7 277 Kodaira dimension of the moduli space of bundles 311 Kodaira vanishing theorem 22 247 Kodaira — Spencer class 156 Kodaira, K. 1 70 131 175 176 186 187 189 249 Koszul complex 32 Kotschick, D. 278 Kronheimer. P. 3 Kummer surface see surface Kummer Lang, S. 275 Leading coefficient of the Donaldson polynomial 240 Lefschetz theorem on (1,1)-classes 18 Lefschetz theorem on hyperplane sections 22 Leray spectral sequence 4 Leung, N. 3 Li, J. 207 308 310 311 Logarithmic transformation 187 Luebke, M. 3 106 Lueroth problem 287 m-sequence 51 Maruyama, M. 3 154 158 162 307 310 Matsumura, H. 4 Mayer, A. 135 Mehta — Ramanathan restriction theorem 246 309 Mehta, V.B. 246 Minimal model 70—71 Minimal model of a threefold 306 Minimal model, relatively 171 Minimal model, strong 71—72 Minimal surface see Surface minimal Miyaoka, Y. 245 Moduli functor 153 Moduli space 153 Moduli space, fine 155 Moishezon, B. 175 189 249 Monads 3 Monoidal transformation 59 Morgan, J.W. 207 240 Mori theory 4 277 279 Mori, S. 4 279 305 Mrowka, T. 3 Mukai, S. 3 310 Multiple fiber 169 Multiplicity 60 Multiplicity of a multiple fiber 169 Mumford's vanishing theorem 22 247 Mumford, D. 1 21 22 72 78 154 246 312 Nagata, M. 91 Nakai — Moishezon criterion 18—21 23 Narasimhan — Seshadri theorem 2 3 105 Narasimhan, M.S. 2 313 Nef divisor see Divisor nef Nef, relatively 172 Noether's formula 9 22 Noether's inequality 281 Normalized degree 85; see Degree normalized Num X 17 Numerically connected see Connected numerically Ogg, A. 194 Okonek, C. 278 Orbifold 188 Orbifold fundamental group 188 Ordinary double point see Double point ordinary Oriented wall 100 O’Grady, K. 240 310—311 Period map 133 297 Picard number 18 Pidstrigach, V. 278 Plurigenera 9 Plurigenera, birational invariance of 62 70 Poincare duality 8 Poincare line bundle 263 Principal homogeneons space 183 Projection formula 24 Projective dimension 51 Projective tangent cone 60 Projectively normal 128 Proper transform 60 Qin, Z. 163 278 Quot scheme 155 Ramanan, S. 2 313 Ramanathan, A. 246 Ramanujam's lemma 191 Rational double point see Double point rational Rational equivalence 28 Rational normal curve 116 Rational ruled surface see Surface rational Rational surface singularity 74—78 80—82 138 Reflexive 45 53—54 56 Reider's theorem 249 274 Reider, I. 248 Relative duality 177 Relative Picard variety 263 Relatively minimal model see Minimal model relatively Representable functor 153 Riemann — Roch theorem 4
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