TY - JOUR
T1 - Building Abelian Functions with Generalised Baker-Hirota Operators
AU - England, Matthew
AU - Athorne, C
PY - 2012
Y1 - 2012
N2 - present a new systematic method to construct Abelian functions on Jacobian varieties of plane, algebraic curves. The main tool used is a symmetric generalisation of the bilinear operator defined in the work of Baker and Hirota. We give explicit formulae for the multiple applications of the operators, use them to define infinite sequences of Abelian functions of a prescribed pole structure and deduce the key properties of these functions. We apply the theory on the two canonical curves of genus three, presenting new explicit examples of vector space bases of Abelian functions. These reveal previously unseen similarities between the theories of functions associated to curves of the same genus.
AB - present a new systematic method to construct Abelian functions on Jacobian varieties of plane, algebraic curves. The main tool used is a symmetric generalisation of the bilinear operator defined in the work of Baker and Hirota. We give explicit formulae for the multiple applications of the operators, use them to define infinite sequences of Abelian functions of a prescribed pole structure and deduce the key properties of these functions. We apply the theory on the two canonical curves of genus three, presenting new explicit examples of vector space bases of Abelian functions. These reveal previously unseen similarities between the theories of functions associated to curves of the same genus.
UR - http://www.scopus.com/inward/record.url?scp=84864107623&partnerID=8YFLogxK
UR - http://arxiv.org/abs/1203.3409
UR - http://dx.doi.org/10.3842/SIGMA.2012.037
U2 - 10.3842/SIGMA.2012.037
DO - 10.3842/SIGMA.2012.037
M3 - Article
SN - 1815-0659
VL - 8
JO - SIGMA: Symmetry, Integrability and Geometry: Methods and Applications
JF - SIGMA: Symmetry, Integrability and Geometry: Methods and Applications
IS - 037
ER -