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  Journal of Algebraic Geometry
Journal of Algebraic Geometry
  
Online ISSN 1534-7486; Print ISSN 1056-3911
 

The Hodge conjecture for general Prym varieties


Authors: Indranil Biswas and Kapil H. Paranjape
Journal: J. Algebraic Geom. 11 (2002), 33-39
Published electronically: November 16, 2001
MathSciNet review: 1865912
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Abstract | References | Additional Information

Abstract: We calculate the Mumford-Tate group of the general Prym variety. As a consequence, the algebra of Hodge cycles is generated by the Néron-Severi.


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

  • 1. Arnaud Beauville, Prym varieties and the Schottky problem, Invent. Math. 41 (1977), no. 2, 149-196.
  • 2. Pierre Deligne, James S. Milne, Arthur Ogus, and Kuang-yen Shih, Hodge cycles, motives, and Shimura varieties, Lecture Notes in Mathematics, no. 900, Springer-Verlag, Berlin, 1982.
  • 3. A. Grothendieck, Hodge's general conjecture is false for trivial reasons, Topology 8 (1969), 299-303.
  • 4. Joe Harris and David Mumford, On the Kodaira dimension of the moduli space of curves, Invent. Math. 67 (1982), no. 1, 23-88, With an appendix by William Fulton.
  • 5. Roger Howe, Remarks on classical invariant theory, Trans. Amer. Math. Soc. 313 (1989), no. 2, 539-570.
  • 6. -, Erratum to: ``Remarks on classical invariant theory'', Trans. Amer. Math. Soc. 318 (1990), no. 2, 823.
  • 7. David Mumford, Prym varieties. I, Contributions to analysis (a collection of papers dedicated to Lipman Bers), 325-350, Academic Press, New-York, 1974.
  • 8. Gian Pietro Pirola, Base number theorem for abelian varieties. An infinitesimal approach, Math. Ann. 282 (1988), no. 3, 361-368.
  • 9. Hermann Weyl, The Classical Groups. Their Invariants and Representations, Princeton University Press, Princeton, N.J., 1939.


Additional Information

Indranil Biswas
Affiliation: School of Mathematics, TIFR, Homi Bhabha Road, Mumbai 400 005, India
Email: indranil@math.tifr.res.in

Kapil H. Paranjape
Affiliation: Institute of Mathematical Sciences, CIT Campus, Tharamani, Chennai 600 113, India
Email: kapil@imsc.ernet.in

DOI: http://dx.doi.org/10.1090/S1056-3911-01-00303-4
PII: S 1056-3911(01)00303-4
Received by editor(s): March 29, 1999
Published electronically: November 16, 2001


Journal of Algebraic Geometry
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