How to compute the genus of $ \{X^4+Y^4+Z^4=0\} \cap \{X^3+Y^3+(Z-tW)^3=0\} \subset \mathbb{P}^3$?
We know that the genus of $ \{X^4+Y^4+Z^4=0\} \subset \mathbb{P}^3$ is 3 because the degree is 4. Now, I want to know the genus of the intersection as a curve. For that I have to use the adjunction formula and the fact that $K_{\mathbb{P}^3}=O(-4)$.