【摘 要】
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Complex functions of two variables with three real-independent periods were studied for the first time by Cousin in 1910 and are at the origin of the theory
【机 构】
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UniversityofPalermo,Italy
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Complex functions of two variables with three real-independent periods were studied for the first time by Cousin in 1910 and are at the origin of the theory of generalized Jacobians.The representation of the generalized Jacobian of a curve as an extension of a linear group by the ordinary Jacobian has been widely investigated by Serre,and since then.It is easy to see that the quotient of CxC modulo a lattice of three real-independent periods is an extension of C* by an elliptic curve.As such,it is also an example of a complex commutative theta group.In this talk,we consider the generalized Jacobian corresponding to this quotient and we bridge these two representations by finding of the modulus(effective divisor)which gives in turn the period lattice,with a purely geometric description.
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