On meromorphic functions defined by a differential system of order 1

Tristan Torrelli

Bulletin de la Société Mathématique de France (2004)

  • Volume: 132, Issue: 4, page 591-612
  • ISSN: 0037-9484

Abstract

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Given a germ h of holomorphic function on ( ℂ n , 0 ) , we study the condition: “the ideal Ann 𝒟 1 / h is generated by operators of order1”. We obtain here full characterizations in the particular cases of Koszul-free germs and unreduced germs of plane curves. Moreover, we prove that this condition holds for a special type of hyperplane arrangements. These results allow us to link this condition to the comparison of de Rham complexes associated with h .

How to cite

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Torrelli, Tristan. "On meromorphic functions defined by a differential system of order $1$." Bulletin de la Société Mathématique de France 132.4 (2004): 591-612. <http://eudml.org/doc/272371>.

@article{Torrelli2004,
abstract = {Given a germ $h$ of holomorphic function on $(\{\mathbb \{C\}\}^n,0)$, we study the condition: “the ideal $\mbox\{\rm Ann\}_\{\mathcal \{D\}\} 1/h$ is generated by operators of order1”. We obtain here full characterizations in the particular cases of Koszul-free germs and unreduced germs of plane curves. Moreover, we prove that this condition holds for a special type of hyperplane arrangements. These results allow us to link this condition to the comparison of de Rham complexes associated with $h$.},
author = {Torrelli, Tristan},
journal = {Bulletin de la Société Mathématique de France},
keywords = {germs of meromorphic functions; $\mathcal \{D\}$-modules; free divisors; arrangements of hyperplanes; logarithmic de Rham complex; logarithmic comparison theorem},
language = {eng},
number = {4},
pages = {591-612},
publisher = {Société mathématique de France},
title = {On meromorphic functions defined by a differential system of order $1$},
url = {http://eudml.org/doc/272371},
volume = {132},
year = {2004},
}

TY - JOUR
AU - Torrelli, Tristan
TI - On meromorphic functions defined by a differential system of order $1$
JO - Bulletin de la Société Mathématique de France
PY - 2004
PB - Société mathématique de France
VL - 132
IS - 4
SP - 591
EP - 612
AB - Given a germ $h$ of holomorphic function on $({\mathbb {C}}^n,0)$, we study the condition: “the ideal $\mbox{\rm Ann}_{\mathcal {D}} 1/h$ is generated by operators of order1”. We obtain here full characterizations in the particular cases of Koszul-free germs and unreduced germs of plane curves. Moreover, we prove that this condition holds for a special type of hyperplane arrangements. These results allow us to link this condition to the comparison of de Rham complexes associated with $h$.
LA - eng
KW - germs of meromorphic functions; $\mathcal {D}$-modules; free divisors; arrangements of hyperplanes; logarithmic de Rham complex; logarithmic comparison theorem
UR - http://eudml.org/doc/272371
ER -

References

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