Some Identities for Abelian Integrals
Copyright policy )Some Identities for Abelian Integrals
The author studies subvarieties in the Jacobi variety of a compact Riemann surface at which certain matrices of second-order theta-functions have exceptionally low ranks. The obtained linear relations between second-order theta-functions involve Abelian integrals and present themselves a natural generalization of Fay's trisecant formula. The various cases of limiting forms of the obtained identities corresponding to coincidences among parameter values are discussed in the paper. Some applications of the results are given; in particular, the relation with Dubrovin identities among theta-nullwerte obtained for explicit solutions of certain nonlinear partial differential equations is clarified.
trisecant formula, Analytic theory of abelian varieties; abelian integrals and differentials, Partial differential equations of mathematical physics and other areas of application, Abelian integrals, theta-nullwerte, Theta functions and abelian varieties, Compact Riemann surfaces and uniformization, Jacobi variety of a compact Riemann surface, Algebraic functions and function fields in algebraic geometry, Jacobians, Prym varieties, second-order theta- functions
trisecant formula, Analytic theory of abelian varieties; abelian integrals and differentials, Partial differential equations of mathematical physics and other areas of application, Abelian integrals, theta-nullwerte, Theta functions and abelian varieties, Compact Riemann surfaces and uniformization, Jacobi variety of a compact Riemann surface, Algebraic functions and function fields in algebraic geometry, Jacobians, Prym varieties, second-order theta- functions
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