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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 $K_{\mathbb{P}^3}=O(-4)$.

  • 2
    WHat do you man by genus in the second paragraph? That is not a curve...2011-04-06
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    Added *algebraic-geometry* tag2011-06-17

2 Answers 2