The Kodaira dimension of spaces of rational curves on low degree hypersurfaces

Details The Kodaira dimension of spaces of rational curves on low degree hypersurfaces The Kodaira dimension of spaces of rational curves on low degree hypersurfaces

2003-05-29

arxiv.org/abs/math/0305432v1

Mathematics

Algebraic Geometry

56 pages

Scientific paper

For a hypersurface in complex projective space $X\subset \PP^n$, we investigate the singularities and Kodaira dimension of the Kontsevich moduli spaces $\Kbm{0,0}{X,e}$ parametrizing rational curves of degree $e$ on $X$. If $d+e \leq n$ and $X$ is a general hypersurface of degree $d$, we prove that $\Kbm{0,0}{X,e}$ has only canonical singularities and we conjecture the same is true for the coarse moduli space $\kbm{0,0}{X,e}$.This investigation is motivated by the question of which Fano hypersurfaces are unirational.

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