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- W2044055796 abstract "Given a covering family $V$ of effective 1-cycles on a complex projective variety $X$, we find conditions allowing to construct a geometric quotient $q~: X to Y$, with $q$ regular on the whole of $X$, such that every fiber of $q$ is an equivalence class for the equivalence relation naturally defined by $V$. Among others, we show that on a normal and $Q$-factorial projective variety $X$ with $dim(X) leq 4$, every covering and quasi-unsplit family $V$ of rational curves generates a geometric extremal ray of the Mori cone $overline{rm NE}(X)$ of classes of effective 1-cycles and that the associated Mori contraction yields a geometric quotient for $V$ provided $X$ has canonical singularities." @default.
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- W2044055796 date "2007-01-01" @default.
- W2044055796 modified "2023-10-04" @default.
- W2044055796 title "On covering and quasi-unsplit families of curves" @default.
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- W2044055796 doi "https://doi.org/10.4171/jems/71" @default.
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