Communications of the Korean Mathematical Society (대한수학회논문집)
- Volume 10 Issue 1
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- Pages.1-10
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- 1995
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- 1225-1763(pISSN)
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- 2234-3024(eISSN)
Heights on singular projective curves
Abstract
In this paper we show that for each divisor class c of degree zero on a projective curve C (not necessarily smooth), there exists a unique function $\hat{h}_c$ on C up to bounded functions. Section 1 contain basic definitions and a brief summary of classical results on Jacobians and heights. In section 2, we prove the existence of "canonical height" on a singular curves and in section 3 we prove the analogouse results on N$\acute{e}$ron functions for singular curves. This is a part of the author's doctorial thesis at Ewha Womens University under the guidence of professor Sung Sik Woo.g Sik Woo.
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