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arXiv · 1709.09740

A note on rational curves on general Fano hypersurfaces

Dennis Tseng
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Abstract

We show 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 the Gromov-Witten invariants in these cases are enumerative.

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Dennis Tseng. 2019-01-31. A note on rational curves on general Fano hypersurfaces. https://arxiv.org/abs/1709.09740

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