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Singularities of theta divisors
and the birational geometry
of irregular varieties


Authors: Lawrence Ein and Robert Lazarsfeld
Journal: J. Amer. Math. Soc. 10 (1997), 243-258
MSC (1991): Primary 14K25, 14J99, 32J27
DOI: https://doi.org/10.1090/S0894-0347-97-00223-3
MathSciNet review: 1396893
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  • [AM] A. Andreotti and A. Mayer, On period relations for abelian integrals on algebraic curves, Ann. Scuola Norm. Sup. Pisa 21 (1967), 189-238. MR 36:3792
  • [AD] E. Arbarello and C. DeConcini, Another proof of a conjecture of S. P. Novikov on periods of abelian integrals on Riemann surfaces, Duke Math. J. 54 (1987), 163-178. MR 88i:14025
  • [De] J.-P. Demailly, $L^{2}$ vanishing theorems for positive line bundles and adjunction theory (to appear).
  • [GL1] M. Green and R. Lazarsfeld, Deformation theory, generic vanishing theorems, and some conjectures of Enriques, Catanese and Beauville, Invent. Math. 90 (1987), 389-407. MR 89b:32025
  • [GL2] -, Higher obstructions to deforming cohomology groups of line bundles, Jour. of A.M.S. 4 (1991), 87-103. MR 92i:32021
  • [Ka] Y. Kawamata, Characterization of abelian varieties, Comp. Math. 43 (1981), 253-276. MR 83j:14029
  • [KMM] Y. Kawamata, K. Matsuda and K. Matsuki, Introduction to the minimal model program, Adv. Study in Pure Math. 10 (1987), 283-360. MR 89e:14015
  • [KV] Y. Kawamata and E. Viehweg, On a characterization of abelian varieties in the classification theory of algebraic varieties, Comp. Math. 41 (1981), 355-360. MR 82c:14028
  • [K] G. Kempf, On the geometry of a theorem of Riemann, Ann. of Math. 98 (1973), 178-185. MR 50:2180
  • [Kol1] J. Kollár, Higher direct images of dualizing sheaves, I, Ann. of Math 123 (1986), 11-42. MR 87c:14038
  • [Kol2] -, Shafarevich maps and plurigenera of algebraic varieties, Invent. Math. 113 (1993), 177-215. MR 94m:14018
  • [Kol3] -, Shafarevich Maps and Automorphic Forms, Princeton Univ. Press, 1995. MR 96i:14016
  • [Kol4] -, Singularities of pairs (to appear).
  • [LB] H. Lange and C. Birkenhake, Complex Abelian Varieties, Springer, 1992. MR 94j:14001
  • [Mori] S. Mori, Classification of higher dimensional varieties, Proc. Symp. Pure Math. 46 (1987), 269-332. MR 89a:14040
  • [Muk] S. Mukai, Duality between $D(X)$ and $D(\hat X)$, with application to Picard sheaves, Nagoya Math. J. 81 (1981), 153-175. MR 82f:14036
  • [Nak] M. Nakamaye, Reducibility of principally polarized abelian varieties with highly singular polarization (to appear).
  • [SV] R. Smith and R. Varley, Multiplicity $g$ points on theta divisors, Duke Math. Jour. 82 (1996), 319-326. CMP 96:12
  • [Var] J. Varouchas, Sur l'image d'une variété Kählérienne compacte, Fonctions de Plusieurs Variables Complexes V, Lecture Notes in Math. 1188 (1986), 245-256. MR 89d:32064
  • [Z] Qi Zhang, Global holomorphic one-forms and Euler characteristics on projective manifolds with ample canonical bundles (to appear).

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Additional Information

Lawrence Ein
Affiliation: Department of Mathematics, University of Illinois at Chicago, Chicago, Illinois 60680
Email: U22425@math.uic.edu

Robert Lazarsfeld
Affiliation: Department of Mathematics, University of California, Los Angeles, California 90024
Email: rkl@math.ucla.edu

DOI: https://doi.org/10.1090/S0894-0347-97-00223-3
Keywords: Singularities, theta divisors, generic vanishing theorem, Albanese mapping
Received by editor(s): March 29, 1996
Received by editor(s) in revised form: June 20, 1996
Additional Notes: The first author was partially supported by N.S.F. Grant DMS 93-02512.\endgraf The second author was partially supported by N.S.F. Grant DMS 94-00815
Article copyright: © Copyright 1997 American Mathematical Society

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