## The Michigan Mathematical Journal

### A Note on Rational Curves on General Fano Hypersurfaces

Dennis Tseng

#### Abstract

We show that the Kontsevich space of rational curves of degree at most roughly $\frac{2-\sqrt{2}}{2}n$ on a general hypersurface $X\subset \mathbb{P}^{n}$ of degree $n-1$ is equidimensional of expected dimension and has two components: one consisting generically of smooth embedded rational curves and the other consisting of multiple covers of a line. This proves more cases of a conjecture of Coskun, Harris, and Starr and shows that the Gromov–Witten invariants in these cases are enumerative.

#### Article information

Source
Michigan Math. J., Advance publication (2019), 20 pages.

Dates
Revised: 1 October 2018
First available in Project Euclid: 6 September 2019

https://projecteuclid.org/euclid.mmj/1567735281

Digital Object Identifier
doi:10.1307/mmj/1567735281

#### Citation

Tseng, Dennis. A Note on Rational Curves on General Fano Hypersurfaces. Michigan Math. J., advance publication, 6 September 2019. doi:10.1307/mmj/1567735281. https://projecteuclid.org/euclid.mmj/1567735281

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