Sheldon Katz has computed this in general in On the finiteness of rational curves on quintic threefolds. See Appendix B on pp. 158-159. He gives a list of the possibilities based on the equations. It is rather simple to check the condition. According to my computation the answer in the above case is $\mathcal O_C(-1)\oplus O_{\mathbb P^1}(-1)\oplus \mathcal O_C(-1)$O_{\mathbb P^1}(-1)$, but it is easy to produce explicit examples with other normal bundles.
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Sheldon Katz has computed this in general in On the finiteness of rational curves on quintic threefolds. See Appendix B on pp. 158-159. You need to do He gives a little work, but given explicit list of the possibilities based on the equations, it's a tedious. It is rather simple to check the condition. According to my computation the answer in the above case is $\mathcal O_C(-1)\oplus \mathcal O_C(-1)$, but it is easy computationto produce explicit examples with other normal bundles. |
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Sheldon Katz has computed this in general in On the finiteness of rational curves on quintic threefolds. See Appendix B on pp. 158-159. You need to do a little work, but given explicit equations, it's a tedious, but easy computation. |
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