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. |
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 ample line bundle anti-involution automorphism cā canonical theta functions coherent sheaf commutative complex torus consider Corollary corresponding curve of genus decomposition defined denote diagram dimension g double covering element elliptic curve embedding Endo(X endomorphism structure equation finite formula functor Hence hermitian form Hodge homomorphism hyperelliptic implies the assertion induces integer intersection involution irreducible isogeny isomorphism Jacobian Let f linear system Math matrix moduli space Moreover morphism multiplication nondegenerate notation Pā Pic(X polarized abelian variety positive definite principally polarized principally polarized abelian Prym variety respect Section sheaf singular smooth projective curve subgroup suffices to show Suppose surjective symplectic basis Theorem theta divisor theta functions theta group theta structure variety of dimension vector bundle vector space
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