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Torsion points on theta divisors


Authors: Robert Auffarth, Gian Pietro Pirola and Riccardo Salvati Manni
Journal: Proc. Amer. Math. Soc. 145 (2017), 89-99
MSC (2010): Primary 14K25; Secondary 32G20
DOI: https://doi.org/10.1090/proc/13230
Published electronically: July 25, 2016
MathSciNet review: 3565362
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Abstract: Using the irreducibility of a natural irreducible representation of the theta group of an ample line bundle on an abelian variety, we derive a bound for the number of $ n$-torsion points that lie on a given theta divisor. We present also two alternate approaches to attacking the case $ n=2$.


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Additional Information

Robert Auffarth
Affiliation: Departamento de Matemáticas, Facultad de Ciencias, Universidad de Chile, Santiago, Chile
Email: rfauffar@mat.puc.cl

Gian Pietro Pirola
Affiliation: Dipartimento di Matematica, Università di Pavia, 27100 Pavia, Italy
Email: gianpietro.pirola@unipv.it

Riccardo Salvati Manni
Affiliation: Dipartimento di Matematica “Guido Castelnuovo”, Università di Roma “La Sapienza”, Rome, Italy
Email: salvati@mat.uniroma1.it

DOI: https://doi.org/10.1090/proc/13230
Keywords: Abelian variety, theta divisor, torsion.
Received by editor(s): March 23, 2016
Published electronically: July 25, 2016
Additional Notes: The authors were partially supported by Fondecyt Grant 3150171, CONICYT PIA ACT1415, Prin 2012 “Moduli Spaces and Lie Theory” and Inadm Gnsaga
Communicated by: Lev Borisov
Article copyright: © Copyright 2016 American Mathematical Society