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

Full-text PDF

References | Similar Articles | Additional Information

**[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,*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 and , 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 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