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Kontsevich spaces of rational curves on Fano hypersurfaces

  • Eric Riedl EMAIL logo and David Yang
Published/Copyright: August 5, 2016

Abstract

We investigate the spaces of rational curves on a general hypersurface. In particular, we show that for a general degree d hypersurface in n with nd+2, the space ¯0,0(X,e) of degree e Kontsevich stable maps from a rational curve to X is an irreducible local complete intersection stack of dimension e(n-d+1)+n-4. This resolves all but one case of a conjecture of Coskun, Harris and Starr, and also proves that the Gromov–Witten invariants of these hypersurfaces are enumerative.

Acknowledgements

We would like to thank Joe Harris, Jason Starr, and Roya Beheshti for helpful conversations. We would also like to thank the anonymous referee for many helpful comments.

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Received: 2015-07-16
Revised: 2016-03-11
Published Online: 2016-08-05
Published in Print: 2019-03-01

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