Degree of the fibres of an elliptic fibration

@article{Buium1983,
abstract = {Let $X\rightarrow B$ an elliptic fibration with general fibre $F$. Let $n_e,n_s,n_a,n_v$ be the minima of the non-zero intersection numbers $(\{\cal L\},F)$ where $\{\cal L\}$ runs successively through the following sets: effective divisors on $X$, invertible sheaves spanned by global sections, ample divisors and very ample divisors. Let $m$ be the maximum of the multiplicities of the fibres of $X\rightarrow B$. We prove that $n_e=n_s$ if and only if $n_e\ge 2m$ and that $n_a=n_v$ if and only if $n_a\ge 3m$.},
author = {Buium, Alexandru},
journal = {Annales de l'institut Fourier},
keywords = {elliptic fibration; intersection numbers; effective divisors; very ample divisors; invertible sheaves},
language = {eng},
number = {1},
pages = {269-276},
publisher = {Association des Annales de l'Institut Fourier},
title = {Degree of the fibres of an elliptic fibration},
url = {http://eudml.org/doc/74572},
volume = {33},
year = {1983},
}

TY - JOUR
AU - Buium, Alexandru
TI - Degree of the fibres of an elliptic fibration
JO - Annales de l'institut Fourier
PY - 1983
PB - Association des Annales de l'Institut Fourier
VL - 33
IS - 1
SP - 269
EP - 276
AB - Let $X\rightarrow B$ an elliptic fibration with general fibre $F$. Let $n_e,n_s,n_a,n_v$ be the minima of the non-zero intersection numbers $({\cal L},F)$ where ${\cal L}$ runs successively through the following sets: effective divisors on $X$, invertible sheaves spanned by global sections, ample divisors and very ample divisors. Let $m$ be the maximum of the multiplicities of the fibres of $X\rightarrow B$. We prove that $n_e=n_s$ if and only if $n_e\ge 2m$ and that $n_a=n_v$ if and only if $n_a\ge 3m$.
LA - eng
KW - elliptic fibration; intersection numbers; effective divisors; very ample divisors; invertible sheaves
UR - http://eudml.org/doc/74572
ER -