Bounds on the denominators in the canonical bundle formula
- [1] IRMA, Université de Strasbourg et CNRS 7 rue René-Descartes 67084 Strasbourg Cedex France
Annales de l’institut Fourier (2013)
- Volume: 63, Issue: 5, page 1951-1969
- ISSN: 0373-0956
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topFloris, Enrica. "Bounds on the denominators in the canonical bundle formula." Annales de l’institut Fourier 63.5 (2013): 1951-1969. <http://eudml.org/doc/275582>.
@article{Floris2013,
abstract = {In this work we study the moduli part in the canonical bundle formula of an lc-trivial fibration whose general fibre is a rational curve. If $r$ is the Cartier index of the fibre, it was expected that $12r$ would provide a bound on the denominators of the moduli part. Here we prove that such a bound cannot even be polynomial in $r$, we provide a bound $N(r)$ and an example where the smallest integer that clears the denominators of the moduli part is $N(r)/r$. Moreover we prove that even locally the denominators depend quadratically on $r$.},
affiliation = {IRMA, Université de Strasbourg et CNRS 7 rue René-Descartes 67084 Strasbourg Cedex France},
author = {Floris, Enrica},
journal = {Annales de l’institut Fourier},
keywords = {lc-trivial fibration; moduli part; denominators; canonical bundle formula},
language = {eng},
number = {5},
pages = {1951-1969},
publisher = {Association des Annales de l’institut Fourier},
title = {Bounds on the denominators in the canonical bundle formula},
url = {http://eudml.org/doc/275582},
volume = {63},
year = {2013},
}
TY - JOUR
AU - Floris, Enrica
TI - Bounds on the denominators in the canonical bundle formula
JO - Annales de l’institut Fourier
PY - 2013
PB - Association des Annales de l’institut Fourier
VL - 63
IS - 5
SP - 1951
EP - 1969
AB - In this work we study the moduli part in the canonical bundle formula of an lc-trivial fibration whose general fibre is a rational curve. If $r$ is the Cartier index of the fibre, it was expected that $12r$ would provide a bound on the denominators of the moduli part. Here we prove that such a bound cannot even be polynomial in $r$, we provide a bound $N(r)$ and an example where the smallest integer that clears the denominators of the moduli part is $N(r)/r$. Moreover we prove that even locally the denominators depend quadratically on $r$.
LA - eng
KW - lc-trivial fibration; moduli part; denominators; canonical bundle formula
UR - http://eudml.org/doc/275582
ER -
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