Complex Abelian VarietiesThis book explores the theory of abelian varieties over the field of complex numbers, explaining both classic and recent results in modern language. The second edition adds five chapters on recent results including automorphisms and vector bundles on abelian varieties, algebraic cycles and the Hodge conjecture. ". . . far more readable than most . . . it is also much more complete." Olivier Debarre in Mathematical Reviews, 1994. |
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Contents
IV | 7 |
VI | 9 |
VII | 13 |
VIII | 15 |
IX | 21 |
X | 23 |
XI | 24 |
XII | 29 |
XCVI | 304 |
XCVII | 308 |
XCVIII | 310 |
XCIX | 315 |
C | 316 |
CI | 322 |
CII | 325 |
CIV | 327 |
XIII | 32 |
XIV | 34 |
XV | 37 |
XVI | 41 |
XVII | 45 |
XVIII | 46 |
XIX | 49 |
XX | 54 |
XXI | 56 |
XXII | 61 |
XXIII | 64 |
XXIV | 66 |
XXV | 69 |
XXVI | 70 |
XXVII | 73 |
XXVIII | 74 |
XXIX | 81 |
XXX | 84 |
XXXI | 88 |
XXXII | 92 |
XXXIII | 97 |
XXXIV | 100 |
XXXV | 102 |
XXXVI | 105 |
XXXVII | 109 |
XXXVIII | 113 |
XXXIX | 114 |
XL | 119 |
XLI | 122 |
XLII | 128 |
XLIII | 131 |
XLIV | 140 |
XLV | 145 |
XLVI | 146 |
XLVII | 149 |
XLVIII | 151 |
XLIX | 153 |
L | 156 |
LI | 159 |
LII | 164 |
LIII | 166 |
LIV | 169 |
LV | 174 |
LVI | 179 |
LVII | 180 |
LVIII | 184 |
LIX | 187 |
LX | 190 |
LXI | 196 |
LXII | 198 |
LXIII | 203 |
LXIV | 209 |
LXV | 210 |
LXVI | 213 |
LXVII | 216 |
LXVIII | 217 |
LXIX | 218 |
LXX | 219 |
LXXI | 220 |
LXXII | 222 |
LXXIII | 227 |
LXXIV | 229 |
LXXV | 232 |
LXXVI | 234 |
LXXVII | 235 |
LXXVIII | 239 |
LXXIX | 243 |
LXXX | 245 |
LXXXI | 246 |
LXXXII | 251 |
LXXXIII | 254 |
LXXXIV | 257 |
LXXXV | 262 |
LXXXVI | 267 |
LXXXVII | 270 |
LXXXVIII | 274 |
LXXXIX | 279 |
XC | 281 |
XCI | 282 |
XCII | 285 |
XCIII | 290 |
XCIV | 293 |
XCV | 300 |
CV | 330 |
CVI | 333 |
CVII | 335 |
CVIII | 337 |
CIX | 341 |
CX | 344 |
CXI | 347 |
CXII | 353 |
CXIII | 359 |
CXIV | 363 |
CXV | 364 |
CXVI | 368 |
CXVII | 372 |
CXVIII | 374 |
CXIX | 378 |
CXX | 381 |
CXXI | 385 |
CXXII | 388 |
CXXIII | 394 |
CXXIV | 399 |
CXXV | 406 |
CXXVI | 411 |
CXXVII | 412 |
CXXVIII | 413 |
CXXIX | 417 |
CXXX | 421 |
CXXXI | 428 |
CXXXII | 431 |
CXXXIII | 436 |
CXXXIV | 439 |
CXXXV | 440 |
CXXXVI | 444 |
CXXXVII | 448 |
CXXXVIII | 453 |
CXXXIX | 455 |
CXL | 459 |
CXLI | 464 |
CXLII | 469 |
CXLIII | 476 |
CXLIV | 479 |
CXLV | 480 |
CXLVI | 484 |
CXLVII | 488 |
CXLVIII | 491 |
CXLIX | 496 |
CL | 503 |
CLI | 507 |
CLII | 512 |
CLIII | 517 |
CLIV | 521 |
CLV | 522 |
CLVI | 525 |
CLVII | 527 |
CLVIII | 532 |
CLIX | 534 |
CLX | 538 |
CLXI | 543 |
CLXII | 546 |
CLXIII | 549 |
CLXIV | 550 |
CLXV | 552 |
CLXVI | 554 |
CLXVII | 559 |
CLXVIII | 561 |
CLXIX | 564 |
CLXX | 567 |
CLXXI | 571 |
CLXXII | 577 |
CLXXIV | 578 |
CLXXV | 579 |
CLXXVI | 580 |
CLXXVIII | 583 |
CLXXX | 587 |
CLXXXI | 589 |
CLXXXII | 591 |
CLXXXIII | 597 |
CLXXXV | 599 |
CLXXXVI | 601 |
CLXXXVII | 603 |
CLXXXVIII | 625 |
631 | |
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Common terms and phrases
abelian subvariety abelian surface According to Lemma According to Proposition algebraically equivalent ample line bundle analytic representation anti-involution automorphism canonical theta functions characteristic coherent sheaf cohomology completes the proof complex torus consider Corollary corresponding curve of genus decomposition defined denote dimension g double covering element elliptic curve embedding endomorphism structure Endq(X equation factor finite formula functor genus g Hence hermitian form Hodge homomorphism hyperelliptic implies the assertion induces integer intersection involution irreducible isogeny isomorphism Jacobian lattice linear system Math moduli space Moreover morphism multiplication nondegenerate notation NS(X Pic(X Poincare bundle polarized abelian variety positive definite principally polarized principally polarized abelian Prym variety Recall respect Section smooth projective curve subgroup subvector space suffices to show Suppose surjective symmetric line bundle symplectic basis theta divisor theta functions theta group theta structure unique variety of dimension vector bundle vector space
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