On the Hodge cycles of Prym varieties

Indranil Biswas[1]

  • [1] School of Mathematics Tata Institute of Fundamental Research Homi Bhabha Road Mumbai 400005, India

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (2004)

  • Volume: 3, Issue: 3, page 625-635
  • ISSN: 0391-173X

Abstract

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We show that the Néron–Severi group of the Prym variety for a degree three unramified Galois covering of a hyperelliptic Riemann surface has a distinguished subgroup of rank three. For the general hyperelliptic curve, the algebra of Hodge cycles on the Prym variety is generated by this group of rank three.

How to cite

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Biswas, Indranil. "On the Hodge cycles of Prym varieties." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 3.3 (2004): 625-635. <http://eudml.org/doc/84543>.

@article{Biswas2004,
abstract = {We show that the Néron–Severi group of the Prym variety for a degree three unramified Galois covering of a hyperelliptic Riemann surface has a distinguished subgroup of rank three. For the general hyperelliptic curve, the algebra of Hodge cycles on the Prym variety is generated by this group of rank three.},
affiliation = {School of Mathematics Tata Institute of Fundamental Research Homi Bhabha Road Mumbai 400005, India},
author = {Biswas, Indranil},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
language = {eng},
number = {3},
pages = {625-635},
publisher = {Scuola Normale Superiore, Pisa},
title = {On the Hodge cycles of Prym varieties},
url = {http://eudml.org/doc/84543},
volume = {3},
year = {2004},
}

TY - JOUR
AU - Biswas, Indranil
TI - On the Hodge cycles of Prym varieties
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 2004
PB - Scuola Normale Superiore, Pisa
VL - 3
IS - 3
SP - 625
EP - 635
AB - We show that the Néron–Severi group of the Prym variety for a degree three unramified Galois covering of a hyperelliptic Riemann surface has a distinguished subgroup of rank three. For the general hyperelliptic curve, the algebra of Hodge cycles on the Prym variety is generated by this group of rank three.
LA - eng
UR - http://eudml.org/doc/84543
ER -

References

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  1. [BN] I. Biswas – M. S. Narasimhan, Hodge classes of moduli spaces of parabolic bundles over the general curve, J. Algebraic Geom. 6 (1997), 697-715. Zbl0891.14002MR1487231
  2. [BP] I. Biswas – K. H. Paranjape, The Hodge conjecture for general Prym varieties, Jour. Alg. Geom. 11 (2002), 33-39. Zbl1060.14044MR1865912
  3. [Ho] R. E. Howe, Remarks on classical invariant theory, Trans. Amer. Math. Soc. 313 (1989), 539-570. Zbl0674.15021MR986027

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