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13 votes
1 answer
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Does a resolution of a rational singularity have rationally connected fibers?

A rational singularity is a singularity of a complex variety $X$ such that for any resolution $\pi:\; \tilde X\rightarrow X$ the higher direct images $R^i\pi_*(O_{\tilde X})$ vanish for all $i>0$. ...
Misha Verbitsky's user avatar
4 votes
1 answer
327 views

Singularities of fibrations

Let $f:X\rightarrow \mathbb{P}^2$ be a fibration, here $X$ is a projective variety of dimension three. Assume that there exixts a smooth curve $C\subset\mathbb{P}^2$ such that for any $p\in\mathbb{P}...
Puzzled's user avatar
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