A construction of the rational function sheaves on elliptic curves

Abstract

The authors introduce an effective method to construct the rational function sheaf $\mathcal{K}$ on an elliptic curve $\mathbb{E}$, and further study the relationship between $\mathcal{K}$ and any coherent sheaf on $\mathbb{E}$. Finally, it is shown that the category of all coherent sheaves of finite length on $\mathbb{E}$ is completely characterized by $\mathcal{K}$.

Keywords

Elliptic curve / Coherent sheaf / Rational function sheaf

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