On the Hodge cycles of Prym varieties
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 3 (2004) no. 3, pp. 625-635.

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.

Classification: 14H40,  14C30
Biswas, Indranil 1

1 School of Mathematics Tata Institute of Fundamental Research Homi Bhabha Road Mumbai 400005, India
@article{ASNSP_2004_5_3_3_625_0,
     author = {Biswas, Indranil},
     title = {On the {Hodge} cycles of {Prym} varieties},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     pages = {625--635},
     publisher = {Scuola Normale Superiore, Pisa},
     volume = {Ser. 5, 3},
     number = {3},
     year = {2004},
     zbl = {1112.14032},
     mrnumber = {2099252},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_2004_5_3_3_625_0/}
}
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
DA  - 2004///
SP  - 625
EP  - 635
VL  - Ser. 5, 3
IS  - 3
PB  - Scuola Normale Superiore, Pisa
UR  - http://www.numdam.org/item/ASNSP_2004_5_3_3_625_0/
UR  - https://zbmath.org/?q=an%3A1112.14032
UR  - https://www.ams.org/mathscinet-getitem?mr=2099252
LA  - en
ID  - ASNSP_2004_5_3_3_625_0
ER  - 
%0 Journal Article
%A Biswas, Indranil
%T On the Hodge cycles of Prym varieties
%J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
%D 2004
%P 625-635
%V Ser. 5, 3
%N 3
%I Scuola Normale Superiore, Pisa
%G en
%F ASNSP_2004_5_3_3_625_0
Biswas, Indranil. On the Hodge cycles of Prym varieties. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 3 (2004) no. 3, pp. 625-635. http://www.numdam.org/item/ASNSP_2004_5_3_3_625_0/

[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. | MR | Zbl

[BP] I. Biswas - K. H. Paranjape, The Hodge conjecture for general Prym varieties, Jour. Alg. Geom. 11 (2002), 33-39. | MR | Zbl

[Ho] R. E. Howe, Remarks on classical invariant theory, Trans. Amer. Math. Soc. 313 (1989), 539-570. | MR | Zbl