2006.414: The problem of differentiation of an Abelian function over its parameters
2006.414: Victor Buchstaber and Dmitry Leykin (2006) The problem of differentiation of an Abelian function over its parameters.
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The present work is devoted to the problem of differentiation of an Abelian function, defined by a family of plane algebraic curves, over the parameters of the family.
A precise formulation of the problem involves the language of Differential Geometry.
We give an effective solution, which is based on our theory of multivariate sigma-function. We obtain explicit expressions for the generators of the module of differentiations of a ring of Abelian functions. This result is equivalent, as we show, to an explicit construction of a Gauss-Manin connection and a Koszul connection in the appropriate vector bundles.
In the course of exposition we outline the key classic results relevant to the problem.
|Item Type:||MIMS Preprint|
|Uncontrolled Keywords:||Abelian fuctions on a Jacobian, plane algebraic curves, Gauss-Manin connection, Coszul connection|
|Subjects:||MSC 2000 > 14 Algebraic geometry|
MSC 2000 > 35 Partial differential equations
MSC 2000 > 53 Differential geometry
|Deposited By:||Dmitry Leykin|
|Deposited On:||14 December 2006|
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