On covering and quasi-unsplit families of curves

Laurent Bonavero; Cinzia Casagrande; Stéphane Druel

Journal of the European Mathematical Society (2007)

  • Volume: 009, Issue: 1, page 45-57
  • ISSN: 1435-9855

Abstract

top
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 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 -factorial projective variety X with canonical singularities and 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 .

How to cite

top

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 -

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.