Embedding Values in word2vec

Are the embedding values for a particular word using word2vec Skipgram model the weights of the first layer or the softmax output of the function? Does the embedding value change according to the training corpus?

$$\DeclareMathOperator{\exp}{exp} p(w_O | w_I) = \frac{\exp({v^{\prime}_{w_O}}^T v_{w_I})}{\sum _{w=1}^W \exp({v^{\prime}_{w}}^T v_{w_I})}$$