Abstract:
By explicitly solving the problem of differentiating hyperelliptic functions with respect to parameters, we derive explicit formulas for the Christoffel symbols of the Gauss–Manin connection in the universal bundle of hyperelliptic curves; as a consequence, we obtain a solution to the problem of differentiating hyperelliptic functions with respect to periods.
Keywords:sigma functions, heat equations, Gauss–Manin connection, universal bundle of hyperelliptic curves, problem of differentiating hyperelliptic functions.
Funding agency
This work was supported by ongoing institutional funding. No additional grants to carry out or direct this particular research were obtained.
Citation:
V. M. Buchstaber, E. Yu. Bunkova, “Formulas for Differentiating Hyperelliptic Functions with Respect to Parameters and Periods”, Geometry, Topology, and Mathematical Physics, Collected papers. Dedicated to Academician Sergei Petrovich Novikov on the occasion of his 85th birthday, Trudy Mat. Inst. Steklova, 325, Steklov Mathematical Institute of RAS, Moscow, 2024, 67–80; Proc. Steklov Inst. Math., 325 (2024), 60–73
\Bibitem{BucBun24}
\by V.~M.~Buchstaber, E.~Yu.~Bunkova
\paper Formulas for Differentiating Hyperelliptic Functions with Respect to Parameters and Periods
\inbook Geometry, Topology, and Mathematical Physics
\bookinfo Collected papers. Dedicated to Academician Sergei Petrovich Novikov on the occasion of his 85th birthday
\serial Trudy Mat. Inst. Steklova
\yr 2024
\vol 325
\pages 67--80
\publ Steklov Mathematical Institute of RAS
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm4387}
\crossref{https://doi.org/10.4213/tm4387}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2024
\vol 325
\pages 60--73
\crossref{https://doi.org/10.1134/S0081543824020032}
Citation in format AMSBIB
Contact us: