The generic \'{ e}taleness is an important property on the moduli space of dormant $\mathfrak{ g}$-opers (for a simple Lie algebra $\mathfrak{ g}$) in the context of enumerative geometry. In the previous study, this property has been verified under the assumption that $\mathfrak{ g}$ is either $\mathfrak{ sl}_\ell$, $\mathfrak{ so}_{ 2\ell -1}$, or $\mathfrak{ sp}_{ 2\ell}$ for any sufficiently small positive integer $\ell$. The purpose of the present paper is to prove the generic \'{ e}taleness for one of the remaining cases, i.e., $\mathfrak{ g} = \mathfrak{ so}_{ 2\ell}$. As an application of this result, we obtain a factorization formula for computing the generic degree induced from pull-back along various clutching morphisms between moduli spaces of pointed stable curves.
Categories: math.AG