On covering and quasi-unsplit families of curves

Bonavero, Laurent, Casagrande, Cinzia, and Druel, Stéphane. "On covering and quasi-unsplit families of curves." Journal of the European Mathematical Society 009.1 (2007): 45-57. <http://eudml.org/doc/277773>.

@article{Bonavero2007,
abstract = {Given a covering family $V$ of effective 1-cycles on a complex projective variety $X$, we find conditions allowing one to construct a geometric quotient $q:X\rightarrow Y$, 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 other results, we show that on a normal and $\mathbb \{Q\}$-factorial projective variety $X$ with canonical singularities and $\operatorname\{dim\}X\le 4$, every covering and quasi-unsplit family $V$ of rational curves generates a geometric extremal ray of the Mori cone $\overline\{\text\{NE\}\}(X)$ of classes of effective 1-cycles and that the associated Mori contraction yields a geometric quotient for $V$.},
author = {Bonavero, Laurent, Casagrande, Cinzia, Druel, Stéphane},
journal = {Journal of the European Mathematical Society},
keywords = {covering families of curves; extremal curves; quotient; Covering families of curves; extremal curves; quotient},
language = {eng},
number = {1},
pages = {45-57},
publisher = {European Mathematical Society Publishing House},
title = {On covering and quasi-unsplit families of curves},
url = {http://eudml.org/doc/277773},
volume = {009},
year = {2007},
}

TY - JOUR
AU - Bonavero, Laurent
AU - Casagrande, Cinzia
AU - Druel, Stéphane
TI - On covering and quasi-unsplit families of curves
JO - Journal of the European Mathematical Society
PY - 2007
PB - European Mathematical Society Publishing House
VL - 009
IS - 1
SP - 45
EP - 57
AB - Given a covering family $V$ of effective 1-cycles on a complex projective variety $X$, we find conditions allowing one to construct a geometric quotient $q:X\rightarrow Y$, 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 other results, we show that on a normal and $\mathbb {Q}$-factorial projective variety $X$ with canonical singularities and $\operatorname{dim}X\le 4$, every covering and quasi-unsplit family $V$ of rational curves generates a geometric extremal ray of the Mori cone $\overline{\text{NE}}(X)$ of classes of effective 1-cycles and that the associated Mori contraction yields a geometric quotient for $V$.
LA - eng
KW - covering families of curves; extremal curves; quotient; Covering families of curves; extremal curves; quotient
UR - http://eudml.org/doc/277773
ER -