Kontsevich spaces of rational curves on Fano hypersurfaces

Abstract

We investigate the spaces of rational curves on a general hypersurface. In particular, we show that for a general degree $d$ hypersurface in ${\mathbb{P}}^n$ with $n\ge d+2$, the space $\overline{{\mathcal{M}}_{0,0}}(X,e)$ of degree $e$ Kontsevich stable maps from a rational curve to $X$ is an irreducible local complete intersection stack of dimension $e(n-d+1)+n-4$.

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References in corpus (3)

• The connectedness of the moduli space of maps to homogeneous spaces
• Fano varieties and linear sections of hypersurfaces
• Rational curves of degree 11 on a general quintic threefold

Cited by in corpus (2)

• On exceptional sets in Manin's Conjecture
• Dimension of the space of conics on Fano hypersurfaces