The Hodge conjecture for general Prym varieties
Authors:
Indranil Biswas and Kapil H. Paranjape
Journal:
J. Algebraic Geom. 11 (2002), 33-39
DOI:
https://doi.org/10.1090/S1056-3911-01-00303-4
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.
Beauville Arnaud Beauville, Prym varieties and the Schottky problem, Invent. Math. 41 (1977), no. 2, 149–196.
DMOS 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.
Hodge A. Grothendieck, Hodge’s general conjecture is false for trivial reasons, Topology 8 (1969), 299–303.
MumfordHarris 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.
Howe1 Roger Howe, Remarks on classical invariant theory, Trans. Amer. Math. Soc. 313 (1989), no. 2, 539–570.
Howe2 ---, Erratum to: “Remarks on classical invariant theory”, Trans. Amer. Math. Soc. 318 (1990), no. 2, 823.
Mumford David Mumford, Prym varieties. I, Contributions to analysis (a collection of papers dedicated to Lipman Bers), 325–350, Academic Press, New-York, 1974.
Pirola Gian Pietro Pirola, Base number theorem for abelian varieties. An infinitesimal approach, Math. Ann. 282 (1988), no. 3, 361–368.
Weyl Hermann Weyl, The Classical Groups. Their Invariants and Representations, Princeton University Press, Princeton, N.J., 1939.
Beauville Arnaud Beauville, Prym varieties and the Schottky problem, Invent. Math. 41 (1977), no. 2, 149–196.
DMOS 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.
Hodge A. Grothendieck, Hodge’s general conjecture is false for trivial reasons, Topology 8 (1969), 299–303.
MumfordHarris 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.
Howe1 Roger Howe, Remarks on classical invariant theory, Trans. Amer. Math. Soc. 313 (1989), no. 2, 539–570.
Howe2 ---, Erratum to: “Remarks on classical invariant theory”, Trans. Amer. Math. Soc. 318 (1990), no. 2, 823.
Mumford David Mumford, Prym varieties. I, Contributions to analysis (a collection of papers dedicated to Lipman Bers), 325–350, Academic Press, New-York, 1974.
Pirola Gian Pietro Pirola, Base number theorem for abelian varieties. An infinitesimal approach, Math. Ann. 282 (1988), no. 3, 361–368.
Weyl 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
MR Author ID:
340073
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
Received by editor(s):
March 29, 1999
Published electronically:
November 16, 2001
