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2 votes
0 answers
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Kodaira dimension of spaces of rational curves in hypersurfaces

Let $X\subset\mathbb{P}^n$ be a general hypersurface of degree $d\leq n$, and $\overline{\mathcal{M}}_{0,0}(X,a)$ the Kontsevich space of degree $a$ rational curves in $X$. Does there exist an ...
4 votes
1 answer
270 views

Blowing-up projective spaces of parametrized rational curves

Consider the projective space $\mathbb{P}^N$ parametrizing morphisms $f:\mathbb{P}^1\rightarrow\mathbb{P}^n$, $f(x,y) = [f_0(x,y):\dots:f_n(x,y)]$ of degree $d$. Let $Z_i\subset\mathbb{P}^N$ be the ...