Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Theta line bundles and the determinant of the Hodge bundle


Author: Alexis Kouvidakis
Journal: Trans. Amer. Math. Soc. 352 (2000), 2553-2568
MSC (2000): Primary 14D05, 14K25, 14L35; Secondary 11F03
DOI: https://doi.org/10.1090/S0002-9947-00-02619-2
Published electronically: February 14, 2000
MathSciNet review: 1709775
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We give an expression of the determinant of the push forward of a symmetric line bundle on a complex abelian fibration, in terms of the pull back of the relative dualizing sheaf via the zero section.


References [Enhancements On Off] (What's this?)

  • [1] Arbarello E. and Cornalba M.: The Picard group of the moduli spaces of curves. Topology 26, 152-171 (1987). MR 88e:14032
  • [2] Barth W., Peters C. and van de Ven A.: Compact Complex Surfaces. Springer-Verlag, 1984. MR 86c:32026
  • [3] Brasch H-J.: Lifting level $D$-structures of abelian varieties. Arch. Math. 60, 553-562 (1993). MR 94b:14038
  • [4] Faltings G. and Chai Ch-L.: Degeneration of Abelian Varieties. Springer-Verlag, 1990. MR 92d:14036
  • [5] Lange H. and Birkenhake Ch.: Complex Abelian Varieties. Springer-Verlag, 1992. MR 94j:14001
  • [6] Moret-Bailly, L.: Pinceaux de variétés abéliennes. Astérisque 129 (1985). MR 87j:14069
  • [7] Mumford D.: Tata Lectures on Theta I. Progress in Mathematics, vol. 28, Birkhäuser, 1983. MR 85h:14026
  • [8] Teixidor i Bigas M.: Half-canonical series on algebraic curves. Transactions of A.M.S. 302, 99-115 (1987). MR 88e:14037
  • [9] Teixidor i Bigas M.: The divisor of curves with a vanishing theta-null. Compositio Math. 66, 15-22 (1988). MR 89c:14040

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 14D05, 14K25, 14L35, 11F03

Retrieve articles in all journals with MSC (2000): 14D05, 14K25, 14L35, 11F03


Additional Information

Alexis Kouvidakis
Affiliation: Department of Mathematics, University of Crete, 71409, Heraklion-Crete, Greece
Email: kouvid@math.uch.gr

DOI: https://doi.org/10.1090/S0002-9947-00-02619-2
Received by editor(s): June 1, 1997
Published electronically: February 14, 2000
Article copyright: © Copyright 2000 American Mathematical Society

American Mathematical Society