Elliptic Curves on Some Homogeneous Spaces

Let $X$ be a minuscule homogeneous space, an odd-dimensional quadric, or an adjoint homogenous space of type different from $A$ and $G_2$. Le $C$ be an elliptic curve. In this paper, we prove that for $d$ large enough, the scheme of degree $d$ morphisms from $C$ to $X$ is irreducible, giving an explicit lower bound for $d$ which is optimal in many cases.

2010 Mathematics Subject Classification: 14M15, 14N35

Keywords and Phrases: Elliptic curves, minuscule homogeneous spaces, adjoint homogeneous spaces.

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