TY - JOUR
T1 - On the symmetric determinantal representations of the Fermat curves of prime degree
AU - Ishitsuka, Yasuhiro
AU - Ito, Tetsushi
N1 - Publisher Copyright:
© 2016 World Scientific Publishing Company.
PY - 2016/6/1
Y1 - 2016/6/1
N2 - We prove that the defining equations of the Fermat curves of prime degree cannot be written as the determinant of symmetric matrices with entries in linear forms in three variables with rational coefficients. In the proof, we use a relation between symmetric matrices with entries in linear forms and non-effective theta characteristics on smooth plane curves. We also use some results of Gross-Rohrlich on the rational torsion points on the Jacobian varieties of the Fermat curves of prime degree.
AB - We prove that the defining equations of the Fermat curves of prime degree cannot be written as the determinant of symmetric matrices with entries in linear forms in three variables with rational coefficients. In the proof, we use a relation between symmetric matrices with entries in linear forms and non-effective theta characteristics on smooth plane curves. We also use some results of Gross-Rohrlich on the rational torsion points on the Jacobian varieties of the Fermat curves of prime degree.
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U2 - 10.1142/S1793042116500597
DO - 10.1142/S1793042116500597
M3 - Article
AN - SCOPUS:84944790598
SN - 1793-0421
VL - 12
SP - 955
EP - 967
JO - International Journal of Number Theory
JF - International Journal of Number Theory
IS - 4
ER -