The dimension of the space of stable maps to the relative Lagrangian Grassmannian over a curve

The dimension of the space of stable maps to the relative Lagrangian Grassmannian over a curve

'Let $C$ be a smooth projective curve and $W$ a symplectic bundle over $C$ of degree $w.$ Let $\pi:\LGW \rightarrow C$ be the relative Lagrangian Grassmannian over $C$ and $\SdW$ be the space of Lagrangian subbundles of degree $w-d$. Then Kontsevich's space $\ocM_g(\LGW,\beta_d)$ of stable maps to $\LGW$ is a compactification of $\SdW$. In this article, we give an upper bound on the dimension of $\ocM_g(\LGW,\beta_d)$, which is an analogue of a result in \cite{PR} for the relative Lagrangian Grassmannian.