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- W1963541346 abstract "Given a morphism between smooth projective varieties $f: W to X$, we study whether $f$-relatively free rational curves imply the existence of $f$-relatively very free rational curves. The answer is shown to be positive when the fibers of the map $f$ have Picard number 1 and a further smoothness assumption is imposed. The main application is when $X subset PP^n$ is a smooth complete intersection of type $(d_1, ..., d_c)$ and $sum d_i^2 leq n$. In this case, we take $W$ to be the space of pointed lines contained in $X$ and the positive answer to the question implies that $X$ contains very twisting ruled surfaces and is strongly rationally simply connected. If the fibers of a smooth family of varieties over a 2-dimensional base satisfy these conditions and the Brauer obstruction vanishes, then the family has a rational section (see cite{dJHS})" @default.
- W1963541346 created "2016-06-24" @default.
- W1963541346 creator A5058373545 @default.
- W1963541346 date "2010-05-07" @default.
- W1963541346 modified "2023-09-27" @default.
- W1963541346 title "Relatively Very Free Curves and Rational Simple Connectedness" @default.
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- W1963541346 hasPublicationYear "2010" @default.
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