Elliptic curves on some homogeneous spaces

Boris Pasquier (1) , Nicolas Perrin (2, 3)

1 I3M - Institut de Mathématiques et de Modélisation de Montpellier
2 HCM - Hausdorff Center for Mathematics
3 IMJ - Institut de Mathématiques de Jussieu

Let $X$ be a minuscule homogeneous space, an odd 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.

Mots clés: Elliptic curves; minuscule homogeneous spaces; adjoint homogeneous spaces

Domaines: Géométrie algébrique [math.AG]

Boris Pasquier, Nicolas Perrin. Elliptic curves on some homogeneous spaces. Documenta Mathematica, 2013, 18, pp.679-706. ⟨hal-00596206⟩