# Remarks on the normal bundles of generic rational curves

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## Abstract

In this note we give a different proof of Sacchiero’s theorem about the splitting type of the normal bundle of a generic rational curve. Moreover we discuss the existence and the construction of smooth monomial curves having generic type of the normal bundle.

### Keywords

Generic rational curve Normal bundle Rational monomial curves### Mathematics Subject Classification

Primary 14C05 Secondary 14H45 14N05## Notes

### Acknowledgements

we wish to thank the referee for the correction and the comments about the pulled back normal bundle \(f^{*}{\mathcal {N}}_{C}\) and for having implicitly stimulated us to prove Theorem 3.

### References

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