Consider a holomorphic embedding $f$ of a genus $g$ Riemann surface $\Sigma_g$ into a generic quintic $Q \subset \mathbb{CP}^4$
This is the same as giving the (very ample) line bundle over the curve $\Sigma_g$
$$ L = f^* \mathcal{O}_{\mathbb{CP}^4}(5) $$
(or should it be $\mathcal{O}(1)$? does this suffice to guarantee the map is to $Q$?)
We can endow both the Riemann surface and $\mathbb{CP}^4$ with antiholomorphic involutions, call them respectively $\Omega$ and $\sigma:(x_1:x_2:x_3:x_4:x_5)\mapsto (\bar x_2:\bar x_1:\bar x_4:\bar x_3:\bar x_5)$ and require $f$ to be equivariant.
(Define also $\mathcal{L}$ as the pointwise fixed locus of $\sigma$ and specify a degree of the map $d=f_*([\Sigma_g])\in H_2(X,\mathcal{L};\mathbb{Z})$.)
QUESTION 1: How is the equivariance requirement translated in terms of line bundles?
Moreover, we can imagine $f$ to develop a node on top of $L$, and then smooth it in different ways.
QUESTION 2: What are the effects of the smoothings in terms of line bundles?