Geodesic
On covering and quasi-unsplit families of curves
Journal of the European Mathematical Society, Tome 9 (2007) no. 1, pp. 45-57

Voir la notice de l'article provenant de la source EMS Press

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→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)≤4, every covering and quasi-unsplit family V of rational curves generates a geometric extremal ray of the Mori cone 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.
DOI : 10.4171/jems/71
Classification : 14-XX, 00-XX
Keywords: Covering families of curves, extremal curves, quotient 
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Laurent Bonavero; Cinzia Casagrande; Stéphane Druel. On covering and quasi-unsplit families of curves. Journal of the European Mathematical Society, Tome 9 (2007) no. 1, pp. 45-57. doi: 10.4171/jems/71

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